The Case of the Mixed-Up Hats

Jun 06, 2015

RAY: There's a baseball team that 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 throw them in a big pile. They fill their little faces with hot dogs and corn on the cob. 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?
RAY: As difficult as it might be for 20 out of 20 to get their hats, it's even harder for 19 out of 20 to get the right hat. In fact, it's impossible, because if 19 kids get the right hat, that leaves only one hat and one head. And it must belong to the other kid.

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! Anyway, who's our winner, Tommy?

TOM: Congratulations to Helen Nye from Montclaire, New Jersey!

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