{"id":6983,"date":"2021-10-22T14:21:43","date_gmt":"2021-10-22T08:51:43","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6983"},"modified":"2021-10-25T01:53:56","modified_gmt":"2021-10-24T20:23:56","slug":"it-is-given-that-the-events-a-and-b-are-such-that-pa-1-4-pa-b-1-2-and-pb-a-2-3-then-pb-is-equal-to","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/it-is-given-that-the-events-a-and-b-are-such-that-pa-1-4-pa-b-1-2-and-pb-a-2-3-then-pb-is-equal-to\/","title":{"rendered":"It is given that the events A and B are such that P(A) = 1\/4, P(A\/B) = 1\/2 and P(B\/A) = 2\/3. Then, P(B) is equal to"},"content":{"rendered":"<h2>Solution :<\/h2>\n<p>We know that,<\/p>\n<p>P(A\/B) = \\(P(A \\cap B)\\over P(B)\\)\u00a0 \u00a0 &#8230;&#8230;.(i)<\/p>\n<p>and P(B\/A) = \\(P(B \\cap A)\\over P(A)\\)\u00a0 \u00a0 &#8230;&#8230;&#8230;.(ii)<\/p>\n<p>\\(\\therefore\\)\u00a0 P(B) = \\(P(B\/A).P(A)\\over P(A\/B)\\) = \\(1\\over 3\\)<\/p>\n<hr \/>\n<h3 style=\"text-align: center;\">Similar Questions<\/h3>\n<p><a class=\"row-title\" 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\/\" aria-label=\"\u201cThe 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\u2019s second win occurs at the third test is\u201d (Edit)\">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\u2019s second win occurs at the third test is<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/a-fair-die-is-tossed-eight-times-the-probability-that-a-third-six-is-observed-on-the-eight-throw-is\/\" aria-label=\"\u201cA fair die is tossed eight times. The probability that a third six is observed on the eight throw, is\u201d (Edit)\">A fair die is tossed eight times. The probability that a third six is observed on the eight throw, is<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/consider-rolling-two-dice-once-calculate-the-probability-of-rolling-a-sum-of-5-or-an-even-sum\/\" aria-label=\"\u201cConsider rolling two dice once. Calculate the probability of rolling a sum of 5 or an even sum.\u201d (Edit)\">Consider rolling two dice once. Calculate the probability of rolling a sum of 5 or an even sum.<\/a><\/p>\n<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/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\/\" aria-label=\"\u201cA 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\u201d (Edit)\">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<p><a class=\"row-title\" href=\"https:\/\/mathemerize.com\/a-die-is-thrown-let-a-be-the-event-that-the-number-obtained-is-greater-than-3-let-b-be-the-event-that-the-number-obtained-is-less-than-5-then-pa-cup-b-is\/\" aria-label=\"\u201cA die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then, \\(P(A \\cup B)\\) is\u201d (Edit)\">A die is thrown. Let A be the event that the number obtained is greater than 3. Let B be the event that the number obtained is less than 5. Then, \\(P(A \\cup B)\\) is<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"<p>Solution : We know that, P(A\/B) = \\(P(A \\cap B)\\over P(B)\\)\u00a0 \u00a0 &#8230;&#8230;.(i) and P(B\/A) = \\(P(B \\cap A)\\over P(A)\\)\u00a0 \u00a0 &#8230;&#8230;&#8230;.(ii) \\(\\therefore\\)\u00a0 P(B) = \\(P(B\/A).P(A)\\over P(A\/B)\\) = \\(1\\over 3\\) Similar Questions The probability of India winning a test match against the west indies is 1\/2 assuming independence from match to match. The probability that &hellip;<\/p>\n<p class=\"read-more\"> <a class=\"\" href=\"https:\/\/mathemerize.com\/it-is-given-that-the-events-a-and-b-are-such-that-pa-1-4-pa-b-1-2-and-pb-a-2-3-then-pb-is-equal-to\/\"> <span class=\"screen-reader-text\">It is given that the events A and B are such that P(A) = 1\/4, P(A\/B) = 1\/2 and P(B\/A) = 2\/3. Then, P(B) is equal to<\/span> Read More &raquo;<\/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":"<!-- This site is optimized with the Yoast SEO plugin v20.12 - https:\/\/yoast.com\/wordpress\/plugins\/seo\/ -->\n<title>It is given that the events A and B are such that P(A) = 1\/4, P(A\/B) = 1\/2 and P(B\/A) = 2\/3. Then, P(B) is equal to<\/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\/it-is-given-that-the-events-a-and-b-are-such-that-pa-1-4-pa-b-1-2-and-pb-a-2-3-then-pb-is-equal-to\/\" \/>\n<meta property=\"og:locale\" content=\"en_US\" \/>\n<meta property=\"og:type\" content=\"article\" \/>\n<meta property=\"og:title\" content=\"It is given that the events A and B are such that P(A) = 1\/4, P(A\/B) = 1\/2 and P(B\/A) = 2\/3. Then, P(B) is equal to\" \/>\n<meta property=\"og:description\" content=\"Solution : We know that, P(A\/B) = (P(A cap B)over P(B))\u00a0 \u00a0 &#8230;&#8230;.(i) and P(B\/A) = (P(B cap A)over P(A))\u00a0 \u00a0 &#8230;&#8230;&#8230;.(ii) (therefore)\u00a0 P(B) = (P(B\/A).P(A)over P(A\/B)) = (1over 3) Similar Questions The probability of India winning a test match against the west indies is 1\/2 assuming independence from match to match. The probability that &hellip; It is given that the events A and B are such that P(A) = 1\/4, P(A\/B) = 1\/2 and P(B\/A) = 2\/3. 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Then, P(B) is equal to","robots":{"index":"index","follow":"follow","max-snippet":"max-snippet:-1","max-image-preview":"max-image-preview:large","max-video-preview":"max-video-preview:-1"},"canonical":"https:\/\/mathemerize.com\/it-is-given-that-the-events-a-and-b-are-such-that-pa-1-4-pa-b-1-2-and-pb-a-2-3-then-pb-is-equal-to\/","og_locale":"en_US","og_type":"article","og_title":"It is given that the events A and B are such that P(A) = 1\/4, P(A\/B) = 1\/2 and P(B\/A) = 2\/3. Then, P(B) is equal to","og_description":"Solution : We know that, P(A\/B) = (P(A cap B)over P(B))\u00a0 \u00a0 &#8230;&#8230;.(i) and P(B\/A) = (P(B cap A)over P(A))\u00a0 \u00a0 &#8230;&#8230;&#8230;.(ii) (therefore)\u00a0 P(B) = (P(B\/A).P(A)over P(A\/B)) = (1over 3) Similar Questions The probability of India winning a test match against the west indies is 1\/2 assuming independence from match to match. The probability that &hellip; It is given that the events A and B are such that P(A) = 1\/4, P(A\/B) = 1\/2 and P(B\/A) = 2\/3. 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