{"id":6964,"date":"2021-10-22T02:16:34","date_gmt":"2021-10-21T20:46:34","guid":{"rendered":"https:\/\/mathemerize.com\/?p=6964"},"modified":"2021-10-25T01:58:44","modified_gmt":"2021-10-24T20:28:44","slug":"if-c-and-d-are-two-events-such-that-c-subset-d-and-pd-ne-0-then-the-correct-statement-among-the-following-is","status":"publish","type":"post","link":"https:\/\/mathemerize.com\/if-c-and-d-are-two-events-such-that-c-subset-d-and-pd-ne-0-then-the-correct-statement-among-the-following-is\/","title":{"rendered":"If C and D are two events such that C \\(\\subset\\) D and P(D) \\(\\ne\\) 0, then the correct statement among the following is"},"content":{"rendered":"

Question :<\/h2>\n

If C and D are two events such that C \\(\\subset\\) D and P(D) \\(\\ne\\) 0, then the correct statement among the following is<\/p>\n

(a) P(C\/D) \\(\\ge\\) P(C)<\/p>\n

(b) P(C\/D) < P(C)<\/p>\n

(c) P(C\/D) = \\(P(D)\\over P(C)\\)<\/p>\n

(d) P(C\/D) = P(C)<\/p>\n

Solution :<\/h2>\n

As P(C\/D) = \\(P(C \\cap D)\\over P(D)\\)<\/p>\n

= \\(P(C)\\over P(D)\\)\u00a0 \u00a0 …….(i)\u00a0 \u00a0 [ \\(\\because\\) C \\(\\subset\\) D]<\/p>\n

Also, as P(D) \\(\\le\\) 1<\/p>\n

\\(\\therefore\\)\u00a0 \\(1\\over P(D)\\) \\(\\ge\\) 1<\/p>\n

and \\(P(C)\\over P(D)\\) \\(\\ge\\) P(C)\u00a0 \u00a0…..(ii)<\/p>\n

P(C\/D) \\(\\ge\\) P(C)<\/p>\n

\n

Similar Questions<\/h3>\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\u2019s second win occurs at the third test is<\/a><\/p>\n

Two aeroplanes I and II bomb a target in succession. The probabilities of I and II scoring a hit correctly are 0.3 and 0.2, respectively. The second plane will bomb only if the first misses the target. The probability that the target is hit by the second plane, is<\/a><\/p>\n

Consider 5 independent Bernoulli\u2019s trials each with probability of success p. If the probability of atleast one failure is greater than or equal to \\(31\\over 32\\), then p lies in the interval<\/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

One ticket is selected at random from 50 tickets numbered 00, 01, 02, \u2026\u2026, 49. Then, the probability that the sum of the digits on the selected ticket is 8, given that the product of these digits is zero equal to<\/a><\/p>\n","protected":false},"excerpt":{"rendered":"

Question : If C and D are two events such that C \\(\\subset\\) D and P(D) \\(\\ne\\) 0, then the correct statement among the following is (a) P(C\/D) \\(\\ge\\) P(C) (b) P(C\/D) < P(C) (c) P(C\/D) = \\(P(D)\\over P(C)\\) (d) P(C\/D) = P(C) Solution : As P(C\/D) = \\(P(C \\cap D)\\over P(D)\\) = \\(P(C)\\over P(D)\\)\u00a0 …<\/p>\n

If C and D are two events such that C \\(\\subset\\) D and P(D) \\(\\ne\\) 0, then the correct statement among the following 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":"\nIf C and D are two events such that C \\(\\subset\\) D and P(D) \\(\\ne\\) 0, then the correct statement among the following 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