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Question

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|(AB))=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 B P(A|B)=13
If X and Y are independent events,
then
P(XY)=P(X)P(Y) and
X and Y are also independent.
So, P(X|Y)=P(XY)P(Y)=P(X)P(Y)P(Y)=P(X)
Therefore, P(A|B)=P(A)=13
and P(A|B)=P(A)=13

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