Question

A couple wants to have children until they have their first daughter, but they will not have more than three children. If the chance of having a child of a particular gender is the same (0.5), find the probability that they will have more boys than girls (note that the sample points are not necessary equiprobable).

Answer 1

Probability that the couple have girl as their first child = 1/2

(In this case they will not have more child's)

Probability that the couple have boy as first child and girl as second child = 1/2 * 1/2 = 1/4

Probability that the couple have boy as first and second child and girl as third child = 1/2 * 1/2 * 1/2 = 1/8

Probability that the couple have boy as all the first three child = 1/8

Thus, in case 3 and 4 the couple will have more boys than girls.

So the required probability = 1/8 + 1/8 = 1/4