Question

Solve the following:

A family has two children. One of them is chosen at random and found that the child is a girl. Find the probability that both the children are girls given that at least one of them is a girl

Answer 1

If the family has two children

the sample space S = {GG, GB, BG, BB}

∴ n(S) = 4

It is given that at least one of them is a girl so that sample space reduces to A = {GG, GB, BG} for which n(A) = 3

Out of these three cases, there is one favourable case GG when both the children are girls.

∴ the required probability = `1/3`