Assume that in a family, each child is equally likely to be a boy or a girl. A family with three children is chosen at random. The probability that the eldest child is a girl given that the family has at least one girl is

We can arrange the statement in set as

S={(B,B,B),(G,G,G),(B,G,G),(G,B,G),(G,G,B),(G,B,B),(B,G,B),(B,B,G)}

Let A be Event that a family has at least one girl then,

A={(G,B,B),(B,G,B),(B,B,G),(G,G,B),(B,G,G)(G,B,G),(G,G,G)

Let B be Event that eldest child is girl then,

B={(G,B,B)(G,G,B),(G,B,G),(G,G,G)

Now, (A ∩ B)={(G,B,B),(G,G,B),(G,B,G,)(G,G,G)

Since,

Hence,