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  4. Let A and B be two events such that the probability that exactly one of them occurs is (2/5) and the probability that A or B occurs is (1/2), then the probability of both of them occur together is :

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Q. Let A and B be two events such that the probability that exactly one of them occurs is $\frac{2}{5}$ and the probability that A or B occurs is $\frac{1}{2}$, then the probability of both of them occur together is :

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Solution:

$P\left(A\right) + P\left(B\right) - 2P\left(A \cap B\right) = \frac{2}{5}$
$P\left(A\right) + P\left(B\right) - P\left(A \cap B\right) = \frac{1}{2}$
$P\left(A \cap B\right) = \frac{1}{10}$