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 `k ^(2),` where `0 lt k lt 1.` Then the probability that at least one of A, B and C occur is:

Options

A. exactly equal to `(1)/(2)`
B. greater than `(1)/(4)` but less than `(1)/(2)`
C. greater than `(1)/(8) ` but less than `(1)/(4)`
D. greater than `(1)/(2)`