Let A and B be two independent events. Statement-1: If P(A)=0.3 and `P(A cup overline(B))=0.8`, then `P(B)=(2)/(7)` Statement-2: For any event `E, P(o

Question

Let A and B be two independent events. Statement-1: If P(A)=0.3 and P(A∪ ˉ B )=0.8, then P(B)= 2 7 Statement-2: For any event E,P( ˉ E )=1-P(E). 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

Answer 1

Correct Answer - A Clearly, statement-2 is true. If A and B are independent events such that P ( A ∪ ¯¯¯ B ) = 0.8 ⇒ 1 − P ( ¯¯¯ A ) P ( ¯¯¯ B ) = 0.8 ⇒ 1 − ( 1 − P ( A ) ) P ( B ) = 0.8 ⇒ 1 − 0.7 P ( B ) = 0.8 ⇒ P ( B ) = 2 7 So, statement-1 is true and statement-2 is a correct explanation for statement-1.