Let `A` ,`B` ,`C` be three events. If the probability of occurring exactly one event out of `A` and `B` is `1-x `, out of `B` and `C` is `1-2x `, out of `C` and `A` is `1-x ` and that of occurring three events simultaneously is `x^2` , then prove that the probability that at least one out of `A`, `B`, `C` will occur is greater than 1/2 .

If A and B are two events,the probability that at most one of these events occurs is

If A, B, C are three events, then what is the probability that at least two of these events occur together?

If A and B are two independent events, then prove that the probability that at least one event will happen will be 1-P(A').P(B') .

If A and B are two events, the probability that exactly one of them occurs is given by

If A and B are two independent events, then the probability that only one of A and B occur is

If A and B are two events, then which of the following does not represent the probability that exactly one of A, B occurs is

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: