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 .

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 occuring three events simultaneously is x^2 , then prove that the probability that atleast one out of A, B, C will occur is greater than 1/2 .

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

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

Let A ,B ,C be three events. If the probability of occurring exactly one event out of Aa n dBi s1-x , out of Ba n dCi s1-2x , out of Ca n dAi s1-x , and that of occuring three events simultaneously is x^2 , then prove that the probability that atleast one out of A, B, C will occur is greaer than 1/2 .

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

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:

If P(A) and P(B) are the probabilities of occurrence of two events A and B, then the probability that exactly one of the two events occur, is