These riddles (specifically, the ones about the boys and the girls) are very subtle and multi-layered. Yes, FeelingLawful (and Mike), you’re correct…it’s 50%; on the other hand, seeing the one girl DOES change quite a bit. It just happens to change things in ways that completely balance out and leave the chance at 50%! As an example of the subtlety, though, let me give you a slight variation of the riddle.
One day, Mike told the riddle in the initial post. Dan, hearing the riddle, said, “The chance that the other child is a girl is 1/2, not 1/3! I’ll even put a little wager on it. I know who lives in every house in Tustin, and I know that you don’t know anyone in Tustin, so you pick a random street, and we’ll go to the first house on that street that has two children living in it, unless the children are both boys. To match the riddle, we can only use houses that have at least one girl.
If the house has TWO girls, you give me $5, but if the house has a boy and a girl, I’ll give you $4.”
If the chance that the other child is a girl is 1/2, then Dan has the good part of the bet – half the time, he gets $5; half the time, he gives up $4.
If the chance that the other child is a girl is 1/3, then Mike has the good part of the bet – he gets $4 twice for every one time he gives up $5.
And even though the answer the original riddle was 1/2, after they repeated this little bet for a few hours, Dan ran out of money…because now the chance was actually 1/3.
Say what?!