If A and B are two events such that P(A)=0.6, P(B)=0.5 and P(A B)=0.4 , then consider the following statements : 1. P( A B)=0.9 . 2. P( B A )=0.6 . Which of the above statements is/are correct?

Step-by-step solution

aligned & P( A )=1-P(A)=1-0.6=0.4 & P( B )=1-P(B)=1-0.5=0.5 aligned Now, P(A B)=P(A)+P(B)-P(A B)=0.6+0.5-0.4=0.7 (1) Now P( A B)=P( A )+P(B)-P( A B) aligned & =P( A )+P(B)- P(B)-P(A B) = & 0.4+0.5- 0.5-0.4 =0.8 aligned Hence, statement (1) is not correct. aligned & (2) P( B A )= P( B A ) P( A ) = P(B A)^ P( A ) = 1-P(A B) P( A ) & = 1-0.7 0.4 =0.75 . aligned Hence, statement (2) is not correct.