If `A and B` are independent events of a random experiment such that `P(A nn B) = 1/6 and P( overlineA nn overlineB)=1/3` then `P(A)=`

Question

If AandB are independent events of a random experiment such that P(A∩B)= 1 6 andP( ˉ A ∩ ˉ B )= 1 3 then P(A)= A. 1 4 B. 1 3 C. 1 6 D. 2 3 Select the correct answer from above options

Answer 1

Correct Answer - B We have, P ( A ∩ B ) = 1 6 and ( ¯¯¯ A ∩ ¯¯¯ B ) = 1 3 P ⇒ P ( A ) P ( B ) = 1 6 and P ( ¯¯¯ A ) P ( ¯¯¯ B ) = 1 3 ⇒ ⇒ x y = 1 6 and ( 1 − x ) ( 1 − y ) = 1 3 ⇒ , where P(A)=x, P(B)=y ⇒ x y = 1 6 and 1 − x − y + 1 6 = 1 3 ⇒ ⇒ x y = 1 6 and x + y = 5 6 ⇒ ⇒ x = 1 2 and y = 1 3 or x = 1 3 and y = 1 2 ⇒