Question:
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 $\mathrm{A}$ or $\mathrm{B}$ occurs is $\frac{1}{2}$, then the probability of both of them occur together is
Correct Option: , 4
Solution:
$\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-2 \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{2}{5}$
$\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{2}$
$\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{10}$
(4) Option
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