If A and B are independent events of a random experiment such that P(A B)= 1 6 and P( A B )= 1 3 , then P(A) is equal to (Here, E is the complement of the event E )

Step-by-step solution

Given that, P(A B)= 1 6 and P( A B )= 1 3 Since, A and B are independent. aligned & P(A) P(B)= 1 6 and P( A ) P( B )= 1 3 & [1-P(A)][1-P(B)]= 1 3 & 1-[P(A)+P(B)]+P(A) P(B)= 1 3 & 1+ 1 6 - 1 3 =P(A)+P(B) & P(A)+P(B)= 5 6 & P(A)= 1 2 , P(B)= 1 3 & and P(A)= 1 3 , P(B)= 1 2 & aligned Hence, options (2) and (3) are correct.