{"id":7035,"date":"2021-10-22T15:44:17","date_gmt":"2021-10-22T10:14:17","guid":{"rendered":"https:\/\/mathemerize.com\/?p=7035"},"modified":"2021-10-25T01:43:40","modified_gmt":"2021-10-24T20:13:40","slug":"the-probability-of-india-winning-a-test-match-against-the-west-indies-is-1-2-assuming-independence-from-match-to-match-the-probability-that-in-a-match-series-indias-second-win-occurs-at-the-third-t","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/the-probability-of-india-winning-a-test-match-against-the-west-indies-is-1-2-assuming-independence-from-match-to-match-the-probability-that-in-a-match-series-indias-second-win-occurs-at-the-third-t\/","title":{"rendered":"The probability of India winning a test match against the west indies is 1\/2 assuming independence from match to match. The probability that in a match series India’s second win occurs at the third test is"},"content":{"rendered":"

Solution :<\/h2>\n

Let \\(A_1\\), \\(A_2\\), \\(A_3\\) be the events of match winning in first, second and third matches respectively and whose probabilities are<\/p>\n

P(\\(A_1\\)) = P(\\(A_2\\)) = P(\\(A_2\\)) = \\(1\\over 2\\)<\/p>\n

\\(\\therefore\\)\u00a0 Required Probability<\/p>\n

= P(\\(A_1\\))P(\\(A_2’\\))P(\\(A_3\\)) + P(\\(A_1’\\))P(\\(A_2\\))P(\\(A_3\\))<\/p>\n

= \\(({1\\over 2})^3\\) + \\(({1\\over 2})^3\\)\u00a0 = \\(1\\over 8\\)\u00a0 + \\(1\\over 8\\) = \\(1\\over 4\\)<\/p>\n

\n

Similar Questions<\/h3>\n

Five horses are in a race. Mr A selects two of the horses at random and bets on them. The probability that Mr A selected the winning horse is<\/a><\/p>\n

A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is<\/a><\/p>\n

If A and B are two mutually exclusive events, then<\/a><\/p>\n

A and B play a game, where each is asked to select a number from 1 to 25. If the two numbers match, both of them win a prize. The probability that they will not win a prize in a single trial is<\/a><\/p>\n

A problem in mathematics is given to three students A, B, C and their respective probability of solving the problem is \\(1\\over 2\\), \\(1\\over 3\\) and \\(1\\over 4\\). Probability that the problem is solved is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Solution : Let \\(A_1\\), \\(A_2\\), \\(A_3\\) be the events of match winning in first, second and third matches respectively and whose probabilities are P(\\(A_1\\)) = P(\\(A_2\\)) = P(\\(A_2\\)) = \\(1\\over 2\\) \\(\\therefore\\)\u00a0 Required Probability = P(\\(A_1\\))P(\\(A_2’\\))P(\\(A_3\\)) + P(\\(A_1’\\))P(\\(A_2\\))P(\\(A_3\\)) = \\(({1\\over 2})^3\\) + \\(({1\\over 2})^3\\)\u00a0 = \\(1\\over 8\\)\u00a0 + \\(1\\over 8\\) = \\(1\\over 4\\) Similar Questions …<\/p>\n

The probability of India winning a test match against the west indies is 1\/2 assuming independence from match to match. The probability that in a match series India’s second win occurs at the third test is<\/span> Read More »<\/a><\/p>\n","protected":false},"author":1,"featured_media":0,"comment_status":"open","ping_status":"closed","sticky":false,"template":"","format":"standard","meta":{"site-sidebar-layout":"default","site-content-layout":"default","ast-global-header-display":"","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":"","theme-transparent-header-meta":"default","adv-header-id-meta":"","stick-header-meta":"","header-above-stick-meta":"","header-main-stick-meta":"","header-below-stick-meta":""},"categories":[43,44],"tags":[],"yoast_head":"\nThe probability of India winning a test match against the west indies is 1\/2 assuming independence from match to match. The probability that in a match series India's second win occurs at the third test is<\/title>\n<meta name=\"robots\" content=\"index, follow, max-snippet:-1, max-image-preview:large, max-video-preview:-1\" \/>\n<link rel=\"canonical\" href=\"https:\/\/mathemerize.com\/the-probability-of-india-winning-a-test-match-against-the-west-indies-is-1-2-assuming-independence-from-match-to-match-the-probability-that-in-a-match-series-indias-second-win-occurs-at-the-third-t\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"The probability of India winning a test match against the west indies is 1\/2 assuming independence from match to match. 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