1. Conditional Probability If two events are not mutually exclusive, the fact that we know that B has happened will have an effect on the probability of A. P(A|B) = P(A B) P(B) P(A|B) is the probability of A given that B has occurred. This formula can be changed to P(B|A) = P(A B) P(A) In order to calculate the probability of B given that A has occurred.

2. Example A sub-committee of 5 is chosen from a committee of 10 men and 8 women. Find the probability of choosing exactly 2 women given that the sub-committee contains at least 1 woman. A - exactly 2 women B – at least 1 woman Possible combinations = 18 C 5 = 8568 8 C 2 x 10 C 3 = 28 x 120 = 3360 P(A B) = 3360 = 20 8568 51 P(A B) = 2 women and at least 1 woman. = 2 women. P(A|B) = P(A B) P(B)

3. 10 C 5 = 252 P(B) =1 - 252 = 33 8568 34 P(A|B) = P(A B) = 20/51 = 40 P(B) 33/34 99 Exercise 3.5 Mathematics Statistics Unit S1 - WJEC Homework 4 P(B) = at least 1 woman = 1 – no women