Let A and B be two events such that probability that exactly one of them occurs is frac{2}{5} and pr

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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

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