If a family has four children is it more likely they will ha

If a family has four children, is it more likely they will have two boys and two girls or three of one sex and one of the other? Assume that the probability of a child being a boy is 1 2 and that the births are independent events.

Solution

Prob of having two boys and two girls = 4C2 * 1/2 * 1/2 * 1/2 * 1/2 = 0.375

Prob of having three of one sex and one of the other = 4C3 * 1/2 * 1/2 * 1/2 * 1/2 * 2 = 0.5

So, it is more likely they will have three of one sex and one of the other.