If A and B are two adjacent events, then prove that the probability of occurance of atleast 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').

If A and B are any two events, then the probability that exactly one of them occur is

If events A and B are independent, then P(A cap B) =

If A and B are any two sets, prove that P(A) = P(B) implies A = B.

A and B are two events such that P(A)!=0, P(B//A) is

If A and B are events such that P(A/B)=P(B/A) , then

If A and B are mutually exclusive events with P(B) ne 1 then P(A|bar B) =

If A and B are any two events having P(A cup B) = 1/2 and P (vec(A)) = 2/3 , then the probability of bar(A) cap B is :

If A and B are independent events such that P(A) gt 0, P(B) gt 0 , then

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.