If A and B are events such that P(A|B) = P(B|A), then - Vidyadip

Question

If A and B are events such that P(A|B) = P(B|A), then

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Answer

It is given that : P( A | B) = P( B | A)
$ \Rightarrow \frac{{P(A \cap B)}}{{P(B)}} = \frac{{P(B \cap A)}}{{P(A)}} $

$\Rightarrow \frac{1}{{P(B)}} = \frac{1}{{P(A)}} \Rightarrow P(A) = P(B) $

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