Assume that each born child 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 the youngest is a girl.

1/2

let b and g represent the boy and the girl child respectively. If a family has two children the sample space will be S= {(b, b), (b, g), (g, b), (g, G)}

Let A be the event that both children are girls.

So, A = {(g, g)}

Let B be the event that the youngest child is a girl.

So, B = {(b, g), (g, g)}

⇒ A∩B = {(g, g)}

So P(B) = 2/4 =1/2

P(A∩B) = 1/4

The conditional probability that both are girls, given that the youngest child is a girl, is given by P(AIB)

P(A/B) = P(A∩B)/ P(B) = (1/4)/(1/2) = 1/2