If A and B are two events such that P ( A B )= 3 4 , P ( A B )= 1 4 , P ( A )= 2 3 where A is the complement of A , then what is P ( B ) equal to?

Step-by-step solution

P ( A B )= 3 4 , P ( A B )= 1 4 aligned & P ( A )= 2 3 P ( A )=1- P ( A ) & P ( A )=1- P ( A )=1- 2 3 = 1 3 aligned P ( A B )= P ( A )+ P ( B )- P ( A B ) aligned & 3 4 = 1 3 + P ( B )- 1 4 & 3 4 + 1 4 - 1 3 = P ( B ) aligned aligned & 4 4 - 1 3 = P ( B ) & P ( B )=1- 1 3 = 2 3 aligned