If A and B are two events such that P( A )=0.3, P(B)=0.4, P(A B )=0.5 , then find the value of P(B / A B )

Step-by-step solution

Given P( A ) = 0.3 , we have P(A) = 1 - 0.3 = 0.7 . Given P(A B ) = 0.5 , we use the identity P(A B ) = P(A) - P(A B) . 0.5 = 0.7 - P(A B) P(A B) = 0.2 . We need to find P(B | A B ) = P(B (A B )) P(A B ) . The numerator is P((B A) (B B )) = P(B A) = P(A B) = 0.2 . The denominator is P(A B ) = P(A) + P( B ) - P(A B ) . Since P(B) = 0.4 , P( B ) = 1 - 0.4 = 0.6 . P(A B ) = 0.7 + 0.6 - 0.5 = 0.8 . Therefore, P(B | A B ) = 0.2 0.8 = 1 4 = 0.25 . Answer: 0.25