Thread: boy/girl problem

This is a pretty standard problem in introductory statistics classes, so if you’ve taken such a class and have seen it before please give others a chance to try to answer before posting the correct answer.

If a couple has two children and one of the children is a boy, what are the odds that the other child is a girl?

For the sake of simplicity let’s ignore biological arguments and assume that for any given birth having a boy or girl is equally likely.

Spoiler (for those to lazy to take the 5 minutes to work it out) :

The probability of the other child being a girl is 1/3. To see why look at the four ways you can have to children

1. Older Girl + younger Girl
2. Older Girl + younger Boy
3. Older Boy + younger Girl
4. Older Boy + younger Boy

Given the data there is only one way out of three possibilities to have a girl in the family.