InterviewSolution
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InterviewSolution
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Let A, B, C be three mutually independen events associated to a random experiment. Statement-1: A and `B cup C` are independent. Statement-2: A and `B cap C` are independent.A. Statement-1 is True, Statement-2 is True, Statement-2 is a correct explanation for Statement-1.B. Statement-1 is True, Statement-2 is True, Statement-2 is not a correct explanation for Statement-1.C. Statement-1 is True, Statement-2 is False.D. Statement-1 is False, Statement-2 is True. |
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Answer» Correct Answer - B IT is given that A, B and C are three mutually, independent events. ` P (A capB) = P (A) P(B),P (B capC), = P(B) P(C)` ` P (C capA) = P(C) P(A) andP (A capB capC) = P(A)P(B)P(C)` Now, ` P(A cap (B cup C))` ` = P {(A cap B) cup ( A cap C)}` ` P ( cap B)+ P ( A cap C) - P {( A cap B) cap ( A cap C))` ` P ( A cap B)+ P ( A cap C) - P ( A cap B cap C)` ` P (A) P (B) + P(A) P(C) - P (A) P (B) P (C)` `P (A) { P(B) + P(C) -P ( B cap C) }` ` P (A)P (B cup C)` A and ` B cup C` are independuct events. Also, ` (A cap B cap C) - P (A) P (B) P (C) = P(A) P ( cap C)` ` Rightarrow A and B cap C` are independent events. |
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