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 ______.

Options

• 0.02

• 0.20

• 0.01

• 0.10

Answer 1

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 0.10.

Explanation:

P(exactly one) = `2/5`

⇒ P(A) + P(B) – 2P(A ∩ B) = `2/5`

P(A or B) = P(A ∪ B) = `1/2`

⇒ P(A) + P(B) – P(A ∩ B) = `1/2`

∴ P(A ∩ B) = `1/2 - 2/5`

= `(5 - 4)/10`

= `1/10`

= 0.10