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14.Probability
hard
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
A
$0.02$
B
$0.01$
C
$0.20$
D
$0.10$
(JEE MAIN-2020)
Solution
$\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-2 \mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{2}{5}$
$\mathrm{P}(\mathrm{A})+\mathrm{P}(\mathrm{B})-\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{2}$
$\mathrm{P}(\mathrm{A} \cap \mathrm{B})=\frac{1}{10}$
Standard 11
Mathematics
