In a sample space events A and B are such that PA PB and PA

In a sample space, events A and B are such that P(A) = P(B) and

          P(A and B) = P(A’ and B’) = p.

          a)       Find P(A).

Solution

from second line, P(A\' and B\') = P((A or B)\') = 1-P(A or B) = p => P(A or B) = 1-p

Now, P(A or B) = P(A) + P(B) - P(A and B)

=> 1-p = 2P(A) - p

=> 1 = 2P(A) => P(A) =1/2