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Statement-1: Let n le 3 " and " A(1), A(...

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_(1) cap overlineA_(2) cap overlineA_(3) cap.. cap overlineA_(n))=(1)/(n+1)`
Statement-2: Let `A_(1), A_(2), A_(3),.., A_(n) " be " n(le 3)` events associated to a random experiment . Then, `A_(1), A_(2),.., A_(n)` are independent iff `P(A_(1) cap A_(2) cap .. cap A_(n))=P(A_(1))P(A_(2))..P(A_(n))`.

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.

Text Solution

Verified by Experts

The correct Answer is:
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 (A_(k) ) = 1/( K+1) " for " k = 1,2,…,n and A_(1) , A_(2) ,..., A_(n) ` are independent then
` P ( overlineA_(1) cap overlineA_(2) cap .... cap overlineA_(n) = P ( overlineA_(1) P overlineA _(2)) ... P ( overlineA_(n))`
` Rightarrow P overline(A_(1)) cap overlineA_(2) cap..... cap overlineA _(n) = 1/2 xx 2/3 xx 3/4 xx .... xx n/ ( n +1) = 1/ ( n +1)`
So, statement -2 is true.
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