NCERT Solutions
Class 12 Maths
Probability

Ex.13.1 Q.12
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 a girl,
(ii) at least one is a girl?
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)}
(i) Let B be the event that the youngest child is a girl.
So, B = {(b, g), (g, g)}
Now, A ∩ B = {(g, g)}
The conditional probability that both are girls, given that the youngest child is a girl, is given by
P (A|B).
So,
Therefore, the required probability is 1/2.
(ii) Let C be the event that at least one child is a girl.
So, C = {(b, g), (g, b), (g, g)}
=> A ∩ C = {(g, g)}
P(C) =
P(A ∩ C) =
The conditional probability that both are girls, given that at least one child is a girl, is given by
P(A|C).
So, P(A|C)