I was just reading this again, and it suddenly reminded me of the three-door paradox. There's a prize behind one door. Pick one. You picked two? Well, let's open three. No prize? That's good. Now, do you want to open the one you picked or the other?

(answer is the other, as long as the other person's selection was random, because the odds are now 50/50 for the other, compared to the 33/66 that you picked the first one with)

So what it comes down to is sort of paradoxical. There are two distinct scenarios, and it does hinge on the word "random" (thanks, Dale!)

If you take a random person with 2 children, there are 4 combinations:

Boy/Boy

Boy/Girl

Girl/Boy

Girl/Girl

For the purposes of this question, we choose a random family. That family has one child who's a boy. That means that it's one of these:

Boy/Boy

Boy/Girl

Girl/Boy

So if one child is a boy, what is the other? 1/3 of the time, it's a boy, and 2/3 of the time, it's a girl.

I don't really understand how it works, the same way I don't really understand how that door problem works, but all I know is, it makes my head hurt trying to think about it.