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

A, B, C are any three events. If P(S) denotes the probability of S happening, then P(A cap (B cup C)) =

For three events A ,B and C ,P (Exactly one of A or B occurs) =P (Exactly one of B or C occurs) =P (Exactly one of C or A occurs) =1/4 and P (All the three events occur simultaneously) =1/16dot Then the probability that at least one of the events occurs, is :

If M and N are any two events, then the probability that exactly one of them occurs is

If A and B are two independent events, then the probability of occurrence of at least one of A and B is given by 1-P'(A)P'(B)

If A and B are two independent events, then the probability of occurrence of at least one of A and B is given by 1" - "P (A') P (B')