Q. 275.0( 1 Vote )

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.

Answer :

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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