Baseball Team Hats
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?
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[ Car Talk Puzzler ]