Suppose that A and B are events defined on a common sample a

Suppose that A and B are events defined on a common sample and that the following probabilities are known P(A) = 0.4, P(B) = 0.3, P(A or B) - 0.66. Find P(A/B).

Solution

P(A | B) = P(A n B) / P(B) ----------------(1)

We have P(A) = 0.4, P(B) = 0.3, P(A u B) = 0.66

P(A n B) = -P(A u B) + P(A) + P(B) = -0.66 + 0.4 + 0.3 = 0.04

From (1) = > P(A | B) = 0.04/0.3 = 0.1333 ~ 0.134