RAY: Hi! We're back. You're listening to Car Talk with us, Click and Clack, the Tappett Brothers, and we're here to talk about cars, car repair, and, duh, the answer to last week's Puzzler.
TOM: It had to do with probability, I understand.
RAY: Probably. This was really geared for the kids in the audience, but since Berman had such a tough time with it, we said adults were eligible to work on it, too. And it is a probability problem. There's this baseball team.
TOM: Oh, I remember.
RAY: That consists of 20 kids, and at the end of the season, the coach decides to have a barbecue at his house. And when the kids arrive, the coach says, listen. I know how you kids love your team and all that, but you can't wear your hats at the barbecue. So, they all tossed their hats into a pile. And they filled their little faces with, you know, hot dogs and hamburgers and the like, and at the end of the party, they all reach in, and at random, they grab a hat and each one puts a hat on his head.
TOM: Mmm-hmm.
RAY: And the question is, what's the probability that 19 out of 20 of these kids gets his original hat? This is a classic case of a little knowledge being a dangerous thing.
TOM: Yes!
RAY: I have no idea how to solve that problem, but I do know --
TOM: That the answer is zero.
RAY: The answer is... In fact, as difficult as it might be for 20 out of 20 to get their hats, it's even harder for 19 --
TOM: Yeah!
RAY: -- out of 20 to get the right hat.
TOM: Yeah.
RAY: In fact, it's impossible, because if 19 kids get the right hat, that leaves only one hat and one head.
TOM: Right.
RAY: And it must belong to --
TOM: The wrong kid.
RAY: -- the other kid.
TOM: Right.
RAY: Louie just got it! All right, Louie!
TOM: If one kid's got the wrong hat, there's gotta be another kid with the wrong hat. It's simple as that.
RAY: Exactly.
TOM: And that's why I got the answer so fast, because I didn't do any calculations, because I don't know how to do any calculations.
RAY: Anyway, who's our winner, Tommy?
TOM: Oh, a winner! The winner is David Krumpe from Penn Hills, Pennsylvania, and for having --[ Car Talk Puzzler ]
