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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

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Let A, B, C be three mutually independen events associated to a random experiment. Statement-1: A and B∪C are independent. Statement-2: A and B∩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. Select the correct answer from above options

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Correct Answer - B IT is given that A, B and C are three mutually, independent events. P(A∩B)=P(A)P(B),P(B∩C),=P(B)P(C) P(C∩A)=P(C)P(A)andP(A∩B∩C)=P(A)P(B)P(C) Now, P(A∩(B∪C)) =P{(A∩B)∪(A∩C)} P(∩B)+P(A∩C)-P{(A∩B)∩(A∩C)) P(A∩B)+P(A∩C)-P(A∩B∩C) P(A)P(B)+P(A)P(C)-P(A)P(B)P(C) P(A){P(B)+P(C)-P(B∩C)} P(A)P(B∪C) A and B∪C are independuct events. Also, (A∩B∩C)-P(A)P(B)P(C)=P(A)P(∩C) ⇒AandB∩C are independent events.

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