Question

Given a family with three ​children, find the probability of the event. The oldest is a boy and the youngest is a girl​, given that there is at least one boy and at least one girl.

Answer 1

The possible cases of the children in increasing order of age are

1) Boy,Boy,Girl

2)Boy,Girl,Boy

3)Girl,Boy,Boy

4)Girl,Girl,Boy

5)Girl,Boy,Girl

6)Boy,Girl,Girl

The favorable cases in our event are 2 numbered 4 and 5

Thus the required probability is

`P(E)=(2)/(6)\\\\P(E)=(1)/(3)`