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 :

Question

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 : (A) 0.10 (B) 0.20 (C) 0.01 (D) 0.02

Tardigrade Admin · Accepted Answer

P(A) + P(B) - 2P(A ∩ B) = (2/5) P(A) + P(B) - P(A ∩ B) = (1/2) P(A ∩ B) = (1/10)

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 :

$0.10$

$0.20$

$0.01$

$0.02$

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

Q. Let A and B be two events such that the probability that exactly one of them occurs is 52​ and the probability that A or B occurs is 21​, then the probability of both of them occur together is :

0.10

0.20

0.01

0.02