> As I see it, there are three options - either it's a boy-boy pair, a girl-girl pair or a boy-girl pair. Yes, but those three options are not equally likely.

> As I see it, there are three options - either it's a boy-boy pair, a girl-girl pair or a boy-girl pair. Yes, but those three options are not equally likely. Let's say the parents decide that their firstborn will be named Jack if male and Jill if female, and the second child will be John if male and Judy if female. Now you see that there are four possibilities: Jack+John, Jack+Judy, Jill+John, Jill+Judy. The last one is eliminated when you know that there is one boy, which gives 1/3 chance that it's the first.