Let A and B be two events such that P(AnB')=0.2, P(A'nB)=0.15, P(A'nB')=0.1, then P(A/B) is equal to

Question : Let A and B be two events such that P(AnB’)=0.2, P(A’nB)=0.15, P(A’nB’)=0.1, then P(A/B) is equal to

(A) 11/14

(B) 2/11

(D) 1/7

Answer : option (A)

Solution :

P(A n B’) = P(A) – P(A n B) = 0.2

Also P(A’ n B) = P(B) – P(A n B) = 0.15

⇒ P(A) + P(B) – 2P(A – B) = 0.35

now, P(A’ n B’) = P(A U B)’ = 1- P(A U B)

⇒ 0.1 = 1 – P(A) – P(B) + P(A n B)

⇒ P(A) + P(B) – P(A n B) = 0.9

⇒ P(A n B) = 0.9 – 0.35 = 0.55 and

P(A) = 0.75, P(B) = 0.7

now, P(A/B) = P(A n B)/P(B) = 0.55/0.7 = 55/70 = 11/14

Let A and B be two events such that P(AnB’)=0.2, P(A’nB)=0.15, P(A’nB’)=0.1, then P(A/B) is equal to