Question

A committee of 4 students is selected at random from a group consisting 8 boys and 4 girls. Given that there is at least one girl on the committee, calculate the probability that there are exactly 2 girls on the committee.

Answer 1

Let A denote the event that at least one girl will be chosen, and B the event that exactly 2 girls will be chosen. We require P (B | A).

Since A denotes the event that at least one girl will be chosen, A denotes that no girl is chosen, i.e., 4 boys are chosen. Then