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 i. the youngest is girl ii. at least one is a girl.

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
i. the youngest is girl

ii. at least one is a girl.

Let B= boy G= girl

And let us consider, in a sample space, the first child is elder and second child is younger.

Total possible outcome = {BB, BG, GB, GG} = 4

Let A= be the event that both the children are girls = 1

Therefore P(A) =

Case 1.

Let B = event that youngest is girl = {BG, GG} =2

{Since we have considered second is younger in a sample space}

Therefore P(B) =

And (A ∩ B) = both are girls and younger is also girl = (GG) = 1

Therefore , P (A ∩ B) =

We require

=

= (answer)

Case 2.

Let B = event that at least one is girl = {BG,GB GG} =3

{Since we have considered second is younger in a sample space}

Therefore P(B) =

And (A ∩ B) = both are girls and atlas one is girl = (GG) = 1

Therefore , P (A ∩ B) =

We require

=

= (answer)

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