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?

Solution

Assume denotes boy and denote girl.

Then, the sample space of the given experiment is Let be the event that ‘both are girls’.

(i) Let be the event that ‘the youngest is a girl’.

Now,

Now, we know that by relation of conditional probability,

and (ii)]

(ii) Assume be the event that ‘at least one is a girl’.

Now,

Now, we know that by relation of conditional probability,