For a particular couple who has one or more children there i

For a particular couple who has one or more children there is a 2/3 probability that the next child will be of the same gender as the preceding one. If a couple has just had their first child and it\'s a boy, what is the probability that their third child from now will be a girl?

Solution

The 1st child of the couple is a boy. The probability that the 2nd child will be a boy is 2/3. Therefore, the probability that the 2nd child will be a girl is 1 - 2/3 = 1/3. The probability that the 3rd child from now will be a girl ( same gender as the preceding child) is ( 2/3) * (1/3) = 2/9