Baseball Team Hats

Jun 03, 2000

RAY: There's a baseball team, which consists of 20 kids. At the end of the season, they all go to the coach's house to have a barbecue. The coach says, "You can't wear your hats at the barbecue." So, all the kids take their hats and they throw them in a big pile.

TOM: I love it! So there are 20 hats in a pile. I can see it coming.

RAY: They fill their little faces with hot dogs and corn on the cob. And, they barf into their hats. At the conclusion of the evening, they all reach in at random, grab a hat and put it on their heads.

What's the probability that 19 out of 20 of these kids get their correct hat?

Answer: 

RAY: 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.

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