Question

Let A, B and C be three events such that the probability that exactly one of A and B occurs is (1 – k), the probability that exactly one of B and C occurs is (1 – 2k), the probability that exactly one of C and A occurs is (1 – k) and the probability of all A, B and C occur simultaneously is k², where 0 < k < 1. Then the probability that at least one of A, B and C occur is :

(1) greater than 1/8 but less than 1/4

(2) greater than 1/2

(3) greater than 1/4 but less than 1/2

(4) exactly equal to 1/2

Answer 1

Answer is: (2) greater than 1/2