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.

Step-by-step solution

P (exactly one) = 2 5 = P A + P B - 2 P A ∩ B = 2 5     . . . 1 P A ∪ B = 1 2 = P A + P B - P A ∩ B = 1 2     . . . 2 ∴ P A ∩ B = 1 2 - 2 5 = 5 - 4 10 = 1 10 .