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

Given that, P [ ( ~A ~B ^ ) ( A ^ B ) ]= 2 5 ...(i) and P(A B)= 1 2 ...(ii) From (i), we get P ( ~A )+ P ( ~B )-2 P ( ~A ~B )= 2 5 ...[From(i)] array ll & P(A B)-P(A B)= 2 5 & 1 2 -P(A B)= 2 5 & P(A B)= 1 2 - 2 5 = 1 10 =0.1 array