What is the probability that a family with three children wi

What is the probability that a family with three children will have:

a) All boys?

b) One girl?

c) Two girls?

Solution

given this (a) P[all boys] = 1/2 x 1/2 x 1/2 = 1/8 (b) one girl could be as BBG, BGB or GBB each with a probability of 1/2 x 1/2 x 1/2 = 1/8 so P[1 girl] = 3/8 (c) P[2 girls] is the same as P[1 boy] due to symmetry, P[2 girls] = 3/8