{"id":103,"date":"2026-08-15T15:29:14","date_gmt":"2026-08-15T15:29:14","guid":{"rendered":"https:\/\/1stmaster.com\/education\/?p=103"},"modified":"2026-08-16T07:47:54","modified_gmt":"2026-08-16T07:47:54","slug":"probability-class-10-important-questions-pyq","status":"publish","type":"post","link":"https:\/\/1stmaster.com\/education\/probability-class-10-important-questions-pyq\/","title":{"rendered":"Probability Class 10 Important Questions PYQ"},"content":{"rendered":"\n<p class=\"wp-block-paragraph\">Probability is the important chapter in the view of CBSE board of class 10th. We provide all the important questions of probability with PYQ. We also provide extra questions with answers so students can check their solution.<\/p>\n\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-1\" class=\"qa-collapse-block__full\">\n\n<h3 class=\"wp-block-heading\">A bag contains 7 black, 5 red and 3 white balls. A ball is drawn from the bag at random. Find the probability that the ball drawn is:<\/h3>\n\n\n\n<ol class=\"wp-block-list\">\n<li>red<\/li>\n\n\n\n<li>black or white<\/li>\n\n\n\n<li>not black<\/li>\n<\/ol>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-1\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-2\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">Given<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">A bag contains:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Black balls = 7<\/li>\n\n\n\n<li>Red balls = 5<\/li>\n\n\n\n<li>White balls = 3<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Total balls = 7 + 5 + 3 = 15<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Probability formula:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mtext>Probability<\/mtext><mo>=<\/mo><mfrac><mtext>Favourable&nbsp;outcomes<\/mtext><mtext>Total&nbsp;outcomes<\/mtext><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Probability} = \\frac{\\text{Favourable outcomes}}{\\text{Total outcomes}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>1. Probability of drawing a red ball<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Favourable outcomes = 5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Red<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>5<\/mn><mn>15<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Red})=\\frac{5}{15}=\\frac{1}{3}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mfrac><mn>1<\/mn><mn>3<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\tfrac{1}{3}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>2. Probability of drawing a black or white ball<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Black or White balls = 7 + 3 = 10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Black&nbsp;or&nbsp;White<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>10<\/mn><mn>15<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Black or White})=\\frac{10}{15}=\\frac{2}{3}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\tfrac{2}{3}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><strong>3. Probability of drawing a ball that is not black<\/strong><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Not black = Red + White = 5 + 3 = 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Not&nbsp;Black<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>8<\/mn><mn>15<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Not Black})=\\frac{8}{15}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mfrac><mn>8<\/mn><mn>15<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\tfrac{8}{15}}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-2\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-3\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A bag contains 7 red, 5 white and 3 black balls. A ball is drawn at random from the bag. Find the probability that the drawn ball is:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>red or white<\/li>\n\n\n\n<li>not black<\/li>\n\n\n\n<li>neither white nor black<\/li>\n<\/ol>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-3\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-4\" class=\"qa-collapse-block__full\">\n\n<h3 class=\"wp-block-heading\">Given<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Red balls = 7<\/li>\n\n\n\n<li>White balls = 5<\/li>\n\n\n\n<li>Black balls = 3<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Total balls = 7 + 5 + 3 = 15<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Formula: Probability = Favourable outcomes \u00f7 Total outcomes<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Probability of drawing a red or white ball<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Red or White balls = 7 + 5 = 12<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Red&nbsp;or&nbsp;White<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>12<\/mn><mn>15<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>4<\/mn><mn>5<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Red or White})=\\frac{12}{15}=\\frac{4}{5}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>4<\/mn><mn>5<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{4}{5}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Probability of drawing a ball that is not black<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Not black = Red + White = 7 + 5 = 12<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Not&nbsp;Black<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>12<\/mn><mn>15<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>4<\/mn><mn>5<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Not Black})=\\frac{12}{15}=\\frac{4}{5}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>4<\/mn><mn>5<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{4}{5}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. Probability of drawing a ball that is neither white nor black<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cNeither white nor black\u201d means red only.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Red balls = 7<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Neither&nbsp;White&nbsp;nor&nbsp;Black<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>7<\/mn><mn>15<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Neither White nor Black})=\\frac{7}{15}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>7<\/mn><mn>15<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{7}{15}}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-4\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-5\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A bag contains 5 red, 4 blue and 3 green balls. A ball is taken out of the bag at random. Find the probability that the selected ball is:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>of red colour<\/li>\n\n\n\n<li>not of green colour<\/li>\n<\/ol>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-5\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-6\" class=\"qa-collapse-block__full\">\n\n<h3 class=\"wp-block-heading\">Given<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Red balls = 5<\/li>\n\n\n\n<li>Blue balls = 4<\/li>\n\n\n\n<li>Green balls = 3<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Total balls = 5 + 4 + 3 = 12<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Probability = Favourable outcomes \u00f7 Total outcomes<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Probability of selecting a red ball<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Favourable outcomes = 5<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Red<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>5<\/mn><mn>12<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Red})=\\frac{5}{12}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>5<\/mn><mn>12<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{5}{12}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Probability of selecting a ball that is not green<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Not green = Red + Blue = 5 + 4 = 9<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Not&nbsp;Green<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>9<\/mn><mn>12<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>3<\/mn><mn>4<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Not Green})=\\frac{9}{12}=\\frac{3}{4}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>3<\/mn><mn>4<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{3}{4}}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-6\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-7\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">Two dice are thrown simultaneously. What is the probability that:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>5 will not come up on either of them?<\/li>\n\n\n\n<li>5 will come up on at least one?<\/li>\n\n\n\n<li>5 will come up at both the dice?<\/li>\n<\/ol>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-7\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-8\" class=\"qa-collapse-block__full\">\n\n<h3 class=\"wp-block-heading\">Given<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Two dice are thrown together.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total number of outcomes = 6 \u00d7 6 = 36<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Sample space = 36 outcomes<\/p>\n\n\n\n<figure class=\"wp-block-table\"><table class=\"has-fixed-layout\"><tbody><tr><th><\/th><th>1<\/th><th>2<\/th><th>3<\/th><th>4<\/th><th>5<\/th><th>6<\/th><\/tr><tr><td>1<\/td><td>(1,1)<\/td><td>(1,2)<\/td><td>(1,3)<\/td><td>(1,4)<\/td><td>(1,5)<\/td><td>(1,6)<\/td><\/tr><tr><td>2<\/td><td>(2,1)<\/td><td>(2,2)<\/td><td>(2,3)<\/td><td>(2,4)<\/td><td>(2,5)<\/td><td>(2,6)<\/td><\/tr><tr><td>3<\/td><td>(3,1)<\/td><td>(3,2)<\/td><td>(3,3)<\/td><td>(3,4)<\/td><td>(3,5)<\/td><td>(3,6)<\/td><\/tr><tr><td>4<\/td><td>(4,1)<\/td><td>(4,2)<\/td><td>(4,3)<\/td><td>(4,4)<\/td><td>(4,5)<\/td><td>(4,6)<\/td><\/tr><tr><td>5<\/td><td>(5,1)<\/td><td>(5,2)<\/td><td>(5,3)<\/td><td>(5,4)<\/td><td>(5,5)<\/td><td>(5,6)<\/td><\/tr><tr><td>6<\/td><td>(6,1)<\/td><td>(6,2)<\/td><td>(6,3)<\/td><td>(6,4)<\/td><td>(6,5)<\/td><td>(6,6)<\/td><\/tr><\/tbody><\/table><\/figure>\n\n\n\n<h3 class=\"wp-block-heading\">1. Probability that 5 will not come up on either die<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A 5 should not appear on both dice.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">On one die, the possible numbers are: 1, 2, 3, 4, 6 (5 outcomes)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, favourable outcomes = 5 \u00d7 5 = 25<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mfrac><mn>25<\/mn><mn>36<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P=\\frac{25}{36}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>25<\/mn><mn>36<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{25}{36}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Probability that 5 will come up on at least one die<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">\u201cAt least one 5\u201d means 5 appears on the first die, or second die, or both.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Favourable outcomes:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>First die = 5 \u2192 6 outcomes<\/li>\n\n\n\n<li>Second die = 5 \u2192 6 outcomes<\/li>\n\n\n\n<li>(5,5) counted twice, so subtract 1<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Total favourable outcomes = 6 + 6 \u2212 1 = 11<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mfrac><mn>11<\/mn><mn>36<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P=\\frac{11}{36}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>11<\/mn><mn>36<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{11}{36}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. Probability that 5 will come up on both dice<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Only one outcome satisfies this: (5,5)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Favourable outcomes = 1<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mfrac><mn>1<\/mn><mn>36<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P=\\frac{1}{36}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>1<\/mn><mn>36<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{1}{36}}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-8\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-9\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A box contains 25 cards numbered from 1 to 25. A card is drawn from the box at random. Find the probability that the number on the drawn card is:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>even<\/li>\n\n\n\n<li>prime<\/li>\n\n\n\n<li>multiple of 6<\/li>\n<\/ol>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-9\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-10\" class=\"qa-collapse-block__full\">\n\n<h3 class=\"wp-block-heading\">Given<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A box contains 25 cards numbered from 1 to 25.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total number of cards = 25<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Formula: Probability = Favourable outcomes \/ Total outcomes<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Probability of drawing an even number<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Even numbers from 1 to 25 are:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2, 4, 6, 8, 10, 12, 14, 16, 18, 20, 22, 24<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Number of even cards = 12<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Even<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>12<\/mn><mn>25<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Even})=\\frac{12}{25}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>12<\/mn><mn>25<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{12}{25}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Probability of drawing a prime number<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Prime numbers from 1 to 25 are:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2, 3, 5, 7, 11, 13, 17, 19, 23<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Number of prime cards = 9<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Prime<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>9<\/mn><mn>25<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Prime})=\\frac{9}{25}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>9<\/mn><mn>25<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{9}{25}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. Probability of drawing a multiple of 6<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Multiples of 6 from 1 to 25 are:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">6, 12, 18, 24<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Number of multiples of 6 = 4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Multiple&nbsp;of&nbsp;6<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>4<\/mn><mn>25<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Multiple of 6})=\\frac{4}{25}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>4<\/mn><mn>25<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{4}{25}}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-10\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-11\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A box contains 19 balls bearing numbers 1, 2, 3, \u2026, 19 respectively. A ball is drawn at random from the box. Find the probability that the number on the ball is:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>a prime number<\/li>\n\n\n\n<li>divisible by 3 or 5<\/li>\n\n\n\n<li>neither divisible by 5 nor by 10<\/li>\n\n\n\n<li>an even number<\/li>\n<\/ol>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-11\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-12\" class=\"qa-collapse-block__full\">\n\n<h3 class=\"wp-block-heading\">Given<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A box contains 19 balls numbered from 1 to 19.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total number of balls = 19<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Formula: <math><semantics><mrow><mtext>Probability<\/mtext><mo>=<\/mo><mfrac><mtext>Favourable&nbsp;outcomes<\/mtext><mtext>Total&nbsp;outcomes<\/mtext><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Probability} = \\frac{\\text{Favourable outcomes}}{\\text{Total outcomes}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Probability of drawing a prime number<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Prime numbers from 1 to 19 are:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2, 3, 5, 7, 11, 13, 17, 19<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Number of prime numbers = 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Prime<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>8<\/mn><mn>19<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Prime})=\\frac{8}{19}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>8<\/mn><mn>19<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{8}{19}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Probability of drawing a number divisible by 3 or 5<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Numbers divisible by 3 or 5 are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Divisible by 3: 3, 6, 9, 12, 15, 18<\/li>\n\n\n\n<li>Divisible by 5: 5, 10, 15<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Common number = 15 (count only once)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Favourable numbers = 3, 5, 6, 9, 10, 12, 15, 18<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Total favourable outcomes = 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mfrac><mn>8<\/mn><mn>19<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P=\\frac{8}{19}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>8<\/mn><mn>19<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{8}{19}}<\/annotation><\/semantics><\/math>198\u200b\u200b<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. Probability of drawing a number neither divisible by 5 nor by 10<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Numbers divisible by 5 or 10 are:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">5, 10, 15<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, numbers neither divisible by 5 nor by 10 = 19 \u2212 3 = 16<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mfrac><mn>16<\/mn><mn>19<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P=\\frac{16}{19}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>16<\/mn><mn>19<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{16}{19}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4. Probability of drawing an even number<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Even numbers from 1 to 19 are:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2, 4, 6, 8, 10, 12, 14, 16, 18<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Number of even numbers = 9<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Even<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>9<\/mn><mn>19<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Even})=\\frac{9}{19}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>9<\/mn><mn>19<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{9}{19}}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-12\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-13\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A box contains 20 balls bearing numbers 1, 2, 3, \u2026, 20 respectively. A ball is drawn at random from the box. What is the probability that the number on the ball is:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>an odd number<\/li>\n\n\n\n<li>divisible by 2 or 3<\/li>\n\n\n\n<li>a prime number<\/li>\n\n\n\n<li>not divisible by 10<\/li>\n<\/ol>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-13\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-14\" class=\"qa-collapse-block__full\">\n\n<h3 class=\"wp-block-heading\">Given<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A box contains 20 balls numbered from 1 to 20.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total number of balls = 20<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Formula:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mtext>Probability<\/mtext><mo>=<\/mo><mfrac><mtext>Favourable&nbsp;Outcomes<\/mtext><mtext>Total&nbsp;Outcomes<\/mtext><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Probability} = \\frac{\\text{Favourable Outcomes}}{\\text{Total Outcomes}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Probability of drawing an odd number<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Odd numbers from 1 to 20 are:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">1, 3, 5, 7, 9, 11, 13, 15, 17, 19<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Number of odd numbers = 10<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Odd<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>10<\/mn><mn>20<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Odd})=\\frac{10}{20}=\\frac{1}{2}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>1<\/mn><mn>2<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{1}{2}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Probability of drawing a number divisible by 2 or 3<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Numbers divisible by 2:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2, 4, 6, 8, 10, 12, 14, 16, 18, 20 (10 numbers)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Numbers divisible by 3:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">3, 6, 9, 12, 15, 18 (6 numbers)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Common numbers (divisible by both 2 and 3):<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">6, 12, 18 (3 numbers)<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, favourable outcomes:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">10 + 6 \u2212 3 = 13<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mfrac><mn>13<\/mn><mn>20<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P=\\frac{13}{20}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>13<\/mn><mn>20<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{13}{20}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. Probability of drawing a prime number<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Prime numbers from 1 to 20 are:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">2, 3, 5, 7, 11, 13, 17, 19<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Number of prime numbers = 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Prime<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>8<\/mn><mn>20<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>2<\/mn><mn>5<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Prime})=\\frac{8}{20}=\\frac{2}{5}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>2<\/mn><mn>5<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{2}{5}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4. Probability of drawing a number not divisible by 10<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Numbers divisible by 10:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">10, 20<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Number of such balls = 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Numbers not divisible by 10 = 20 \u2212 2 = 18<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mfrac><mn>18<\/mn><mn>20<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>9<\/mn><mn>10<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P=\\frac{18}{20}=\\frac{9}{10}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>9<\/mn><mn>10<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{9}{10}}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-14\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-15\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">Find the probability of getting 53 Fridays in a leap year.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-15\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-16\" class=\"qa-collapse-block__full\">\n\n<h3 class=\"wp-block-heading\">Step 1: Total number of days in a leap year<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A leap year has 366 days.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mn>366<\/mn><mo>=<\/mo><mn>52<\/mn><mtext>&nbsp;weeks<\/mtext><mo>+<\/mo><mn>2<\/mn><mtext>&nbsp;days<\/mtext><\/mrow><annotation encoding=\"application\/x-tex\">366=52\\text{ weeks}+2\\text{ days}<\/annotation><\/semantics><\/math>366=52&nbsp;weeks+2&nbsp;days<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, every weekday occurs 52 times, and the remaining 2 days occur 53 times.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Possible extra days<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">The two extra days can be:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>Monday &amp; Tuesday<\/li>\n\n\n\n<li>Tuesday &amp; Wednesday<\/li>\n\n\n\n<li>Wednesday &amp; Thursday<\/li>\n\n\n\n<li>Thursday &amp; Friday<\/li>\n\n\n\n<li>Friday &amp; Saturday<\/li>\n\n\n\n<li>Saturday &amp; Sunday<\/li>\n\n\n\n<li>Sunday &amp; Monday<\/li>\n<\/ol>\n\n\n\n<p class=\"wp-block-paragraph\">There are 7 equally likely possibilities.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Favourable outcomes<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A leap year has 53 Fridays if Friday is one of the two extra days.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">This happens in 2 cases:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Thursday &amp; Friday<\/li>\n\n\n\n<li>Friday &amp; Saturday<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Favourable outcomes = 2<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 4: Probability<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mn>53<\/mn><mtext>&nbsp;Fridays<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>2<\/mn><mn>7<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(53\\text{ Fridays})=\\frac{2}{7}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>2<\/mn><mn>7<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{2}{7}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Probability of getting 53 Fridays in a leap year = <math><semantics><mrow><mfrac><mn>2<\/mn><mn>7<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{2}{7}<\/annotation><\/semantics><\/math>.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-16\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-17\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">If the probability of winning a game is 0.6, what is the probability of losing it?<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-17\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-18\" class=\"qa-collapse-block__full\">\n\n<h3 class=\"wp-block-heading\">Given<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Probability of winning = 0.6<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">We know:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Winning<\/mtext><mo stretchy=\"false\">)<\/mo><mo>+<\/mo><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Losing<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Winning})+P(\\text{Losing})=1<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Calculation<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Losing<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mn>1<\/mn><mo>\u2212<\/mo><mn>0.6<\/mn><mo>=<\/mo><mn>0.4<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Losing})=1-0.6=0.4<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Probability of losing the game = <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mn>0.4<\/mn><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{0.4}<\/annotation><\/semantics><\/math>\u200b or <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mstyle displaystyle=\"false\" scriptlevel=\"0\"><mfrac><mn>2<\/mn><mn>5<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\tfrac{2}{5}}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-18\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-19\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">One card is drawn from a well-shuffled deck of 52 cards. Find the probability of drawing:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>an ace<\/li>\n\n\n\n<li>a 4 of spades<\/li>\n\n\n\n<li>a 9 of a black suit<\/li>\n\n\n\n<li>a red king<\/li>\n<\/ol>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-19\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-20\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">Given: A well-shuffled deck has 52 cards.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Formula:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mtext>Probability<\/mtext><mo>=<\/mo><mfrac><mtext>Number&nbsp;of&nbsp;favourable&nbsp;outcomes<\/mtext><mtext>Total&nbsp;number&nbsp;of&nbsp;outcomes<\/mtext><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Probability} = \\frac{\\text{Number of favourable outcomes}}{\\text{Total number of outcomes}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Probability of drawing an ace<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Number of aces = 4<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Ace<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>4<\/mn><mn>52<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>13<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Ace})=\\frac{4}{52}=\\frac{1}{13}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>1<\/mn><mn>13<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{1}{13}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Probability of drawing the 4 of spades<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Only one 4 of spades<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>4&nbsp;of&nbsp;Spades<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><mn>52<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{4 of Spades})=\\frac{1}{52}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>1<\/mn><mn>52<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{1}{52}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. Probability of drawing a 9 of a black suit<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Black suits are Spades and Clubs.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Black 9s = 9\u2660 and 9\u2663 = 2 cards<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>9&nbsp;of&nbsp;a&nbsp;black&nbsp;suit<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>2<\/mn><mn>52<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>26<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{9 of a black suit})=\\frac{2}{52}=\\frac{1}{26}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>1<\/mn><mn>26<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{1}{26}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4. Probability of drawing a red king<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Red suits are Hearts and Diamonds.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Red kings = 2<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Red&nbsp;King<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>2<\/mn><mn>52<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>26<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Red King})=\\frac{2}{52}=\\frac{1}{26}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>1<\/mn><mn>26<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{1}{26}}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-20\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-21\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A card is drawn at random from a well-shuffled deck of 52 cards. Find the probability of getting:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>a queen<\/li>\n\n\n\n<li>a diamond<\/li>\n\n\n\n<li>a king or an ace<\/li>\n\n\n\n<li>a red ace<\/li>\n<\/ol>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-21\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-22\" class=\"qa-collapse-block__full\">\n\n<h3 class=\"wp-block-heading\">Given<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">A well-shuffled deck has 52 playing cards.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total number of cards = 52<\/li>\n\n\n\n<li>Probability = Favourable outcomes \/ Total outcomes<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">1. Probability of drawing an Ace<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">There are 4 Aces in a deck.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Ace<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>4<\/mn><mn>52<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>13<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Ace})=\\frac{4}{52}=\\frac{1}{13}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>1<\/mn><mn>13<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{1}{13}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Probability of drawing the 4 of Spades<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">There is only one 4 of Spades.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mn>4<\/mn><mtext>&nbsp;of&nbsp;Spades<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>1<\/mn><mn>52<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(4\\text{ of Spades})=\\frac{1}{52}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>1<\/mn><mn>52<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{1}{52}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. Probability of drawing a 9 of a black suit<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Black suits are Spades and Clubs.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">The black 9s are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>9 of Spades<\/li>\n\n\n\n<li>9 of Clubs<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Favourable cards = 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Black&nbsp;9<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>2<\/mn><mn>52<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>26<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Black 9})=\\frac{2}{52}=\\frac{1}{26}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>1<\/mn><mn>26<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{1}{26}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4. Probability of drawing a Red King<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Red suits are Hearts and Diamonds.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Red Kings are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>King of Hearts<\/li>\n\n\n\n<li>King of Diamonds<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Favourable cards = 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Red&nbsp;King<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>2<\/mn><mn>52<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>26<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Red King})=\\frac{2}{52}=\\frac{1}{26}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>1<\/mn><mn>26<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{1}{26}}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-22\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-23\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A card is drawn at random from a well-shuffled pack of 52 cards. Find the probability that the card drawn is neither a red card nor a queen.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-23\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-24\" class=\"qa-collapse-block__full\">\n\n<h3 class=\"wp-block-heading\">Given<\/h3>\n\n\n\n<h3 class=\"wp-block-heading\">Given<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total number of cards = 52<\/li>\n\n\n\n<li>Red cards = 26<\/li>\n\n\n\n<li>Queens = 4<\/li>\n\n\n\n<li>Red queens = 2 (Queen of Hearts and Queen of Diamonds)<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Step 1: Find the cards that are red or queens<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Since the 2 red queens are counted twice, subtract them once.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mn>26<\/mn><mo>+<\/mo><mn>4<\/mn><mo>\u2212<\/mo><mn>2<\/mn><mo>=<\/mo><mn>28<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">26+4-2=28<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, 28 cards are either red or queens.<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 2: Find the cards that are neither red nor queens<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mn>52<\/mn><mo>\u2212<\/mo><mn>28<\/mn><mo>=<\/mo><mn>24<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">52-28=24<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Favourable outcomes = 24<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Step 3: Find the probability<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo>=<\/mo><mfrac><mn>24<\/mn><mn>52<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>6<\/mn><mn>13<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P=\\frac{24}{52}=\\frac{6}{13}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Final Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>6<\/mn><mn>13<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{6}{13}}<\/annotation><\/semantics><\/math>136\u200b\u200b<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-24\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-25\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A card is drawn at random from a pack of 52 playing cards. Find the probability that the card drawn is neither a queen nor a jack.<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-25\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-26\" class=\"qa-collapse-block__full\">\n\n<h3 class=\"wp-block-heading\">Solution<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Total number of cards = 52<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Queens in a pack = 4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Jacks in a pack = 4<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Therefore, cards that are queens or jacks = 4 + 4 = 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cards that are neither queen nor jack:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mn>52<\/mn><mo>\u2212<\/mo><mn>8<\/mn><mo>=<\/mo><mn>44<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">52-8=44<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Probability<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Neither&nbsp;Queen&nbsp;nor&nbsp;Jack<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>44<\/mn><mn>52<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>11<\/mn><mn>13<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Neither Queen nor Jack})=\\frac{44}{52}=\\frac{11}{13}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-26\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-27\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A card is drawn at random from a well-shuffled deck of playing cards. Find the probability that the card drawn is:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>a card of spades or an ace<\/li>\n\n\n\n<li>a red king<\/li>\n\n\n\n<li>either a king or a queen<\/li>\n\n\n\n<li>neither a king nor a queen<\/li>\n<\/ol>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-27\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-28\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A well-shuffled deck contains 52 playing cards.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Spades = 13 cards<\/li>\n\n\n\n<li>Hearts = 13 cards<\/li>\n\n\n\n<li>Diamonds = 13 cards<\/li>\n\n\n\n<li>Clubs = 13 cards<\/li>\n\n\n\n<li>Kings = 4 cards<\/li>\n\n\n\n<li>Queens = 4 cards<\/li>\n\n\n\n<li>Aces = 4 cards<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Formula: Probability = Favourable Outcomes \/ Total Outcomes<\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Probability of drawing a spade or an ace<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Number of spades = 13<\/li>\n\n\n\n<li>Number of aces = 4<\/li>\n\n\n\n<li>Common card (Ace of Spades) = 1<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mtext>Favourable&nbsp;outcomes<\/mtext><mo>=<\/mo><mn>13<\/mn><mo>+<\/mo><mn>4<\/mn><mo>\u2212<\/mo><mn>1<\/mn><mo>=<\/mo><mn>16<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Favourable outcomes}=13+4-1=16<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Spade&nbsp;or&nbsp;Ace<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>16<\/mn><mn>52<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>4<\/mn><mn>13<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Spade or Ace})=\\frac{16}{52}=\\frac{4}{13}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>4<\/mn><mn>13<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{4}{13}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Probability of drawing a red king<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Red suits are Hearts and Diamonds.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Red kings are:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>King of Hearts<\/li>\n\n\n\n<li>King of Diamonds<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Favourable outcomes = 2<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Red&nbsp;King<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>2<\/mn><mn>52<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>26<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Red King})=\\frac{2}{52}=\\frac{1}{26}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>1<\/mn><mn>26<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{1}{26}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. Probability of drawing either a king or a queen<\/h3>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Kings = 4<\/li>\n\n\n\n<li>Queens = 4<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">A card cannot be both a king and a queen.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Favourable outcomes = 4 + 4 = 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>King&nbsp;or&nbsp;Queen<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>8<\/mn><mn>52<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>2<\/mn><mn>13<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{King or Queen})=\\frac{8}{52}=\\frac{2}{13}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>2<\/mn><mn>13<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{2}{13}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">4. Probability of drawing neither a king nor a queen<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Cards that are kings or queens = 8<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Cards that are neither = 52 \u2212 8 = 44<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Neither&nbsp;King&nbsp;nor&nbsp;Queen<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>44<\/mn><mn>52<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>11<\/mn><mn>13<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Neither King nor Queen})=\\frac{44}{52}=\\frac{11}{13}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>11<\/mn><mn>13<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{11}{13}}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-28\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-29\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">The king, queen, jack and 10, all of spades, are lost from a pack of 52 playing cards. A card is drawn from the remaining well-shuffled pack. Find the probability of getting:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>a red card<\/li>\n\n\n\n<li>king<\/li>\n\n\n\n<li>black card<\/li>\n<\/ol>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-29\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-30\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total cards in a pack = 52<\/li>\n\n\n\n<li>Lost cards = King, Queen, Jack and 10 of Spades = 4 cards<\/li>\n\n\n\n<li>Remaining cards = 52 \u2212 4 = 48<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Formula:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mtext>Probability<\/mtext><mo>=<\/mo><mfrac><mtext>Number&nbsp;of&nbsp;favourable&nbsp;outcomes<\/mtext><mtext>Total&nbsp;number&nbsp;of&nbsp;outcomes<\/mtext><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Probability} = \\frac{\\text{Number of favourable outcomes}}{\\text{Total number of outcomes}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Probability of getting a red card<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">All red cards are still present.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Red cards = 26<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Red&nbsp;card<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>26<\/mn><mn>48<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>13<\/mn><mn>24<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Red card})=\\frac{26}{48}=\\frac{13}{24}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>13<\/mn><mn>24<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{13}{24}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Probability of getting a king<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">There are 4 kings originally, but the King of Spades is lost.<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Kings left = 3<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>King<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>3<\/mn><mn>48<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>16<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{King})=\\frac{3}{48}=\\frac{1}{16}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>1<\/mn><mn>16<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{1}{16}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. Probability of getting a black card<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Originally black cards = 26<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Four spade cards are lost, so:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Black cards left = 26 \u2212 4 = 22<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Black&nbsp;card<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>22<\/mn><mn>48<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>11<\/mn><mn>24<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Black card})=\\frac{22}{48}=\\frac{11}{24}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>11<\/mn><mn>24<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{11}{24}}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-30\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-31\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">Red kings, queens and jacks are removed from a deck of 52 playing cards and then well-shuffled. A card is drawn from the remaining cards. Find the probability of getting:<\/p>\n\n\n\n<ol class=\"wp-block-list\">\n<li>a king<\/li>\n\n\n\n<li>a red card<\/li>\n\n\n\n<li>a spade<\/li>\n<\/ol>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-31\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-32\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A standard deck has 52 cards.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Removed cards: Red Kings, Red Queens, and Red Jacks<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Red Kings = 2<\/li>\n\n\n\n<li>Red Queens = 2<\/li>\n\n\n\n<li>Red Jacks = 2<\/li>\n<\/ul>\n\n\n\n<p class=\"wp-block-paragraph\">Total removed = 6 cards<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">So, remaining cards = 52 \u2212 6 = 46<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Probability = <math><semantics><mrow><mfrac><mtext>Favourable&nbsp;outcomes<\/mtext><mn>46<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{\\text{Favourable outcomes}}{46}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">1. Probability of getting a king<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Originally there are 4 kings. Two red kings are removed, so 2 black kings remain.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>King<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>2<\/mn><mn>46<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>1<\/mn><mn>23<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{King})=\\frac{2}{46}=\\frac{1}{23}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>1<\/mn><mn>23<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{1}{23}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">2. Probability of getting a red card<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Originally there are 26 red cards. Six red face cards are removed.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Red cards left = 26 \u2212 6 = 20<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Red<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>20<\/mn><mn>46<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>10<\/mn><mn>23<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Red})=\\frac{20}{46}=\\frac{10}{23}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>10<\/mn><mn>23<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{10}{23}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">3. Probability of getting a spade<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">No spade is removed, so all 13 spades remain.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>P<\/mi><mo stretchy=\"false\">(<\/mo><mtext>Spade<\/mtext><mo stretchy=\"false\">)<\/mo><mo>=<\/mo><mfrac><mn>13<\/mn><mn>46<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">P(\\text{Spade})=\\frac{13}{46}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Answer: <math><semantics><mrow><menclose notation=\"box\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"false\"><mstyle scriptlevel=\"0\" displaystyle=\"true\"><mfrac><mn>13<\/mn><mn>46<\/mn><\/mfrac><\/mstyle><\/mstyle><\/mstyle><\/menclose><\/mrow><annotation encoding=\"application\/x-tex\">\\boxed{\\frac{13}{46}}<\/annotation><\/semantics><\/math><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-32\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--question wp-block-qa-collapse-blocks-question\" data-word-limit=\"2500\" data-kind=\"question\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Question<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-33\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">A bag contains 27 balls, of which some are white and the others are red. A ball is chosen at random. The probability of getting a red ball is 2\/3. Find the number of white balls.<br><\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-33\" hidden>Show More<\/button><\/section>\n\n<section class=\"qa-collapse-block qa-collapse-block--answer wp-block-qa-collapse-blocks-answer\" data-word-limit=\"1500\" data-kind=\"answer\" data-join-next=\"false\"><div class=\"qa-collapse-block__header\"><span class=\"qa-collapse-block__badge\">Answer<\/span><span class=\"qa-collapse-block__number\" aria-hidden=\"true\"><\/span><\/div><div id=\"qa-collapse-content-34\" class=\"qa-collapse-block__full\">\n\n<p class=\"wp-block-paragraph\">Given:<\/p>\n\n\n\n<ul class=\"wp-block-list\">\n<li>Total number of balls = 27<\/li>\n\n\n\n<li>Probability of getting a red ball = 2\/3<\/li>\n<\/ul>\n\n\n\n<h3 class=\"wp-block-heading\">Formula<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mtext>Probability<\/mtext><mo>=<\/mo><mfrac><mtext>Number&nbsp;of&nbsp;favourable&nbsp;outcomes<\/mtext><mtext>Total&nbsp;number&nbsp;of&nbsp;outcomes<\/mtext><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\text{Probability} = \\frac{\\text{Number of favourable outcomes}}{\\text{Total number of outcomes}}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Let the number of red balls be R.<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mfrac><mi>R<\/mi><mn>27<\/mn><\/mfrac><mo>=<\/mo><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><\/mrow><annotation encoding=\"application\/x-tex\">\\frac{R}{27}=\\frac{2}{3}<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mi>R<\/mi><mo>=<\/mo><mfrac><mn>2<\/mn><mn>3<\/mn><\/mfrac><mo>\u00d7<\/mo><mn>27<\/mn><mo>=<\/mo><mn>18<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">R=\\frac{2}{3}\\times 27=18<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<p class=\"wp-block-paragraph\">Number of white balls:<\/p>\n\n\n\n<p class=\"wp-block-paragraph\"><math display=\"block\"><semantics><mrow><mn>27<\/mn><mo>\u2212<\/mo><mn>18<\/mn><mo>=<\/mo><mn>9<\/mn><\/mrow><annotation encoding=\"application\/x-tex\">27-18=9<\/annotation><\/semantics><\/math><\/p>\n\n\n\n<h3 class=\"wp-block-heading\">Answer<\/h3>\n\n\n\n<p class=\"wp-block-paragraph\">Number of white balls = 9<\/p>\n\n<\/div><button class=\"qa-collapse-block__toggle\" type=\"button\" aria-expanded=\"true\" aria-controls=\"qa-collapse-content-34\" hidden>Show More<\/button><\/section>","protected":false},"excerpt":{"rendered":"<p>Probability is the important chapter in the view of CBSE board of class 10th. We provide all the important questions [&hellip;]<\/p>\n","protected":false},"author":1,"featured_media":108,"comment_status":"open","ping_status":"open","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"","ast-site-content-layout":"default","site-content-style":"default","site-sidebar-style":"default","ast-global-header-display":"","ast-banner-title-visibility":"","ast-main-header-display":"","ast-hfb-above-header-display":"","ast-hfb-below-header-display":"","ast-hfb-mobile-header-display":"","site-post-title":"","ast-breadcrumbs-content":"","ast-featured-img":"","footer-sml-layout":"","ast-disable-related-posts":"","theme-transparent-header-meta":"","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":"","astra-migrate-meta-layouts":"default","ast-page-background-enabled":"default","ast-page-background-meta":{"desktop":{"background-color":"var(--ast-global-color-5)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"ast-content-background-meta":{"desktop":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"tablet":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""},"mobile":{"background-color":"var(--ast-global-color-4)","background-image":"","background-repeat":"repeat","background-position":"center center","background-size":"auto","background-attachment":"scroll","background-type":"","background-media":"","overlay-type":"","overlay-color":"","overlay-opacity":"","overlay-gradient":""}},"footnotes":""},"categories":[3],"tags":[],"class_list":["post-103","post","type-post","status-publish","format-standard","has-post-thumbnail","hentry","category-class-10"],"aioseo_notices":[],"aioseo_head":"\n\t\t<!-- All in One SEO 5.0.0.1 - aioseo.com -->\n\t<meta name=\"description\" content=\"Probability is the important chapter in the view of CBSE board of class 10th. We provide all the important questions of probability with PYQ. We also provide extra questions with answers so students can check their solution. A bag contains 7 black, 5 red and 3 white balls. A ball is drawn from the bag\" \/>\n\t<meta name=\"robots\" content=\"max-image-preview:large\" \/>\n\t<meta name=\"author\" content=\"1st Master\"\/>\n\t<link rel=\"canonical\" href=\"https:\/\/1stmaster.com\/education\/probability-class-10-important-questions-pyq\/\" \/>\n\t<meta name=\"generator\" content=\"All in One SEO (AIOSEO) 5.0.0.1\" \/>\n\t\t<meta name=\"twitter:card\" content=\"summary_large_image\" \/>\n\t\t<meta name=\"twitter:title\" content=\"Probability Class 10 Important Questions PYQ\" \/>\n\t\t<meta name=\"twitter:description\" content=\"Probability is the important chapter in the view of CBSE board of class 10th. We provide all the important questions of probability with PYQ. We also provide extra questions with answers so students can check their solution. A bag contains 7 black, 5 red and 3 white balls. A ball is drawn from the bag\" \/>\n\t\t<meta name=\"twitter:image\" content=\"https:\/\/1stmaster.com\/education\/wp-content\/uploads\/2026\/08\/1st-master-education-logo-1.webp\" \/>\n\t\t<!-- All in One SEO -->\n\n","aioseo_head_json":{"title":"Probability Class 10 Important Questions PYQ","description":"Probability is the important chapter in the view of CBSE board of class 10th. We provide all the important questions of probability with PYQ. We also provide extra questions with answers so students can check their solution. A bag contains 7 black, 5 red and 3 white balls. A ball is drawn from the bag","canonical_url":"https:\/\/1stmaster.com\/education\/probability-class-10-important-questions-pyq\/","robots":"max-image-preview:large","keywords":"","webmasterTools":{"miscellaneous":""},"schema":null,"twitter:card":"summary_large_image","twitter:title":"Probability Class 10 Important Questions PYQ","twitter:description":"Probability is the important chapter in the view of CBSE board of class 10th. We provide all the important questions of probability with PYQ. We also provide extra questions with answers so students can check their solution. A bag contains 7 black, 5 red and 3 white balls. A ball is drawn from the bag","twitter:image":"https:\/\/1stmaster.com\/education\/wp-content\/uploads\/2026\/08\/1st-master-education-logo-1.webp"},"aioseo_meta_data":{"post_id":"103","title":null,"description":null,"keywords":null,"keyphrases":{"focus":{"keyphrase":"","score":0,"analysis":{"keyphraseInTitle":{"score":0,"maxScore":9,"error":1}}},"additional":[]},"focus_keyword":null,"additional_keywords":null,"truseo_locale":null,"primary_term":null,"canonical_url":null,"og_title":null,"og_description":null,"og_object_type":"default","og_image_type":"default","og_image_custom_url":null,"og_image_custom_fields":null,"og_image_url":null,"og_image_width":null,"og_image_height":null,"og_video":"","og_custom_url":null,"og_article_section":null,"og_article_tags":null,"twitter_use_og":false,"twitter_card":"default","twitter_image_type":"default","twitter_image_custom_url":null,"twitter_image_custom_fields":null,"twitter_image_url":null,"twitter_title":null,"twitter_description":null,"schema_type":"default","schema_type_options":null,"schema":{"blockGraphs":[],"customGraphs":[],"default":{"data":{"Article":[],"Course":[],"Dataset":[],"FAQPage":[],"Movie":[],"Person":[],"Product":[],"ProductReview":[],"Car":[],"Recipe":[],"Service":[],"SoftwareApplication":[],"WebPage":[]},"graphName":"BlogPosting","isEnabled":true},"graphs":[]},"pillar_content":false,"robots_default":true,"robots_noindex":false,"robots_noarchive":false,"robots_nosnippet":false,"robots_nofollow":false,"robots_noimageindex":false,"robots_noodp":false,"robots_notranslate":false,"robots_max_snippet":"-1","robots_max_videopreview":"-1","robots_max_imagepreview":"large","priority":null,"frequency":"default","local_seo":null,"limit_modified_date":false,"ai":{"faqs":[],"keyPoints":[],"schemas":[],"titles":[],"descriptions":[],"socialPosts":{"email":{"subject":"","preview":"","content":""},"linkedin":[],"twitter":[],"facebook":[],"instagram":[]}},"breadcrumb_settings":null,"seo_analyzer_scan_date":null,"created":"2026-08-16 01:59:21","updated":"2026-08-16 08:13:27"},"aioseo_breadcrumb":"<div class=\"aioseo-breadcrumbs\"><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/1stmaster.com\/education\" title=\"Home\">Home<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">&raquo;<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\t<a href=\"https:\/\/1stmaster.com\/education\/category\/class-10\/\" title=\"Class 10\">Class 10<\/a>\n\t\t<\/span><span class=\"aioseo-breadcrumb-separator\">&raquo;<\/span><span class=\"aioseo-breadcrumb\">\n\t\t\tProbability Class 10 Important Questions PYQ\n\t\t<\/span><\/div>","aioseo_breadcrumb_json":[{"label":"Home","link":"https:\/\/1stmaster.com\/education"},{"label":"Class 10","link":"https:\/\/1stmaster.com\/education\/category\/class-10\/"},{"label":"Probability Class 10 Important Questions PYQ","link":"https:\/\/1stmaster.com\/education\/probability-class-10-important-questions-pyq\/"}],"_links":{"self":[{"href":"https:\/\/1stmaster.com\/education\/wp-json\/wp\/v2\/posts\/103","targetHints":{"allow":["GET"]}}],"collection":[{"href":"https:\/\/1stmaster.com\/education\/wp-json\/wp\/v2\/posts"}],"about":[{"href":"https:\/\/1stmaster.com\/education\/wp-json\/wp\/v2\/types\/post"}],"author":[{"embeddable":true,"href":"https:\/\/1stmaster.com\/education\/wp-json\/wp\/v2\/users\/1"}],"replies":[{"embeddable":true,"href":"https:\/\/1stmaster.com\/education\/wp-json\/wp\/v2\/comments?post=103"}],"version-history":[{"count":10,"href":"https:\/\/1stmaster.com\/education\/wp-json\/wp\/v2\/posts\/103\/revisions"}],"predecessor-version":[{"id":141,"href":"https:\/\/1stmaster.com\/education\/wp-json\/wp\/v2\/posts\/103\/revisions\/141"}],"wp:featuredmedia":[{"embeddable":true,"href":"https:\/\/1stmaster.com\/education\/wp-json\/wp\/v2\/media\/108"}],"wp:attachment":[{"href":"https:\/\/1stmaster.com\/education\/wp-json\/wp\/v2\/media?parent=103"}],"wp:term":[{"taxonomy":"category","embeddable":true,"href":"https:\/\/1stmaster.com\/education\/wp-json\/wp\/v2\/categories?post=103"},{"taxonomy":"post_tag","embeddable":true,"href":"https:\/\/1stmaster.com\/education\/wp-json\/wp\/v2\/tags?post=103"}],"curies":[{"name":"wp","href":"https:\/\/api.w.org\/{rel}","templated":true}]}}