Assume that each child born is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that

Question

Assume that each child born is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that at least one is a girl?

Philoid · Accepted Answer

At least one is a girl

Let C be the event that at least one is a girl

Then C = {(b, g), (g, b), (g, g)}, n(C) = 3

And the corresponding probability becomes

The sample space for the both girls is girl child and at least one is a girl will become

(A∩C) = {(g, g)}, n(A∩C)=1

And the corresponding probability becomes

So the conditional probability that both are girls given that the youngest is a girl is

Assume that each child born is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given thatat least one is a girl?

Assume that each child born is equally likely to be a boy or a girl. If a family has two children, what is the conditional probability that both are girls given that
at least one is a girl?