Ignoring semantical quibbles for a moment, the knowledge that one child is a girl is not irrelevant to the scenarios. This knowledge eliminates the boy-boy scenario. Likewise, knowing that one child is a boy eliminates the girl-girl scenario.
If you know that *exactly *one child is a boy, then the options are as follows:
- older child boy, younger child girl
- older child girl, younger child boy
So yes, the odds are one out of two, or 50-50, of the oldest being a boy.
However, saying “one child is a boy” does not necessarily mean that only one child is a boy. In mathematics you have to be very exact and say something like “exactly one child is a boy” or “one and only one child is a boy”.
Yes, whereas in English if you say “one child is a boy” the default assumption is that the other child is not.
Sorry, yes, my semantics were out to lunch. :smack:
“Exactly one child is a boy” - odds oldest is a boy is 50-50. (BG or GB)
“At least one child is a boy” - odds oldest is a boy - 2 in 3 (BB, BG, GB).
In the “Exactly…” case, the definition of “one is a boy” conveys no information that determines order. It does, however, eliminate the cases BB and GG so the odds are still 50-50. The “at least…” case is basically the original one, one child walks into a room…
A few people in this thread have said the boy/girl problem as usually stated (and as stated in Cecil’s column) is ambiguous. I disagree that it is ambiguous in any interesting way relevant to the puzzle, and I definitively explained exactly why it’s not ambiguous here. Unfortunately no one has ever acknowledged the definitiveness of my argument in that post. But there it is.