I spent a good part of yesterday puzzling over this, published on Jason Rosenhouse's EvolutionBlog (and getting involved in the surprisingly enthusiastic debate over it):
"A shopkeeper says she has two new baby beagles to show you, but she doesn't know whether they're both male, both female, or one of each. You tell her that you want only a male, and she telephones the fellow who's giving them a bath. “Is at least one a male?” she asks him. She receives a reply. “Yes!” she informs you with a smile. What is the probability that the other one is a male?"
At the moment, I'm firmly in the "p = 1/3" camp - after initially putting an argument for "p = 1/2" - but I'm anxiously awaiting Rosenhouse's analysis. So far, he's just let us debate it back and forth.
I find these sorts of probability puzzles fascinating, but they often make me feel as if my head is spinning. It took me a full day to convince myself that the solution to the famous Monty Hall problem is correct, after my pal Chris Lawson introduced the problem and the solution to me some years ago. There was a similar problem (wish I could remember the details) doing the rounds at the AAP conference earlier this year, and I never did manage to bring myself to agree with the most popular solution - although I'm willing to concede I was probably overlooking, or not getting, something ... and that the popular solution was sponsored by better logicians than me.