Statement-1: Let `n le 3 " and " A_(1), A_(2),.., A_(n)` be n independent events such that `P(A_(k))=(1)/(k+1) " for " 1 le k le n`, then `P(overlineA

Question

Statement-1: Let n≤3 and A1,A2,..,An be n independent events such that P(Ak)= 1 k+1 for 1≤k≤n, then P( ˉ A 1∩ ˉ A 2∩ ˉ A 3∩..∩ ˉ A n)= 1 n+1 Statement-2: Let A1,A2,A3,..,An be n(≤3) events associated to a random experiment . Then, A1,A2,..,An are independent iff P(A1∩A2∩..∩An)=P(A1)P(A2)..P(An). 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 - C We know that three or more events associated toa randon experiment are independent iff they are pairwise independent as well as independent together. So, statement -2 is not true. If P(Ak)= 1 K+1 for k=1,2,…,nandA1,A2,...,An are independent then P( ˉ A 1∩ ˉ A 2∩....∩ ˉ A n=P( ˉ A 1P ˉ A 2)...P( ˉ A n) ⇒P ¯ A1 ∩ ˉ A 2∩.....∩ ˉ A n= 1 2 × 2 3 × 3 4 ×....× n n+1 = 1 n+1 So, statement -2 is true.