Question

there are 6 women and 5 men on a committee. What is the probability that all three people selected are women, given that all three selected are the same gender?

Answer 1

Number of ways of selecting all three the same gender = 6C3 + 5C3 = 20 + 10 = 30
The probability that all three people selected are women, given that all three selected are the same gender = 6C3 / (6C3 + 5C3) = 20 / 30 = 2/3