Let A and B be two independent events such that P(A)=13 and P(B)=16. Then, which of the following is TRUE ?
A
P(A|(A∪B))=14
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B
P(A|B′)=13
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C
P(A|B)=23
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D
P(A′|B′)=13
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Solution
The correct option is BP(A|B′)=13 If X and Y are independent events, then P(X∩Y)=P(X)P(Y) and X and Y′ are also independent. So, P(X|Y)=P(X∩Y)P(Y)=P(X)P(Y)P(Y)=P(X) Therefore, P(A|B)=P(A)=13 and P(A|B′)=P(A)=13