Q. 2 A4.3( 4 Votes )

# 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 thatthe youngest is a girl,

Let b and g represents the boy and the girl child respectively.

Now if a family has two children, the sample space will be

S = {(b, b), (b, g), (g, b), (g, g)}, n(S)=4

Let A be the event that both children are girls, the

A= {(g, g)}, n(A)=1

So the probability that both children are girls is

If the youngest is a girl

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

Then B = {(b, g), (g, g)}, n(B) = 2

And the corresponding probability becomes

The sample space for the both girls is girl child and the youngest is a girl will become

(AB) = {(g, g)}, n(AB)=1

And the corresponding probability becomes

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

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