JEE PYQ: Probability Question 28
Question 28 - 2020 (08 Jan Shift 2)
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:
(1) $0.02$
(2) $0.20$
(3) $0.01$
(4) $0.10$
Show Answer
Answer: (4)
Solution
$P(A) + P(B) - 2P(A \cap B) = \frac{2}{5}$ and $P(A) + P(B) - P(A \cap B) = \frac{1}{2}$. Subtracting: $P(A \cap B) = \frac{1}{2} - \frac{2}{5} = \frac{1}{10} = 0.10$.
BETA
