It has been said that people do not have a very good intuitive sense of probability. When I first saw the following problem, I was very surprised when I saw the answer.

At a restaurant, the hatcheck person completely messes up and loses track of which hat belongs to which person. When people go to get their hats, they are given a hat at random. For around 20 hats, what would you say is the best approximation to the probability that not a single person gets the correct hat?

1/1000
1/10
⅓
½
⅔
9/10
999/1000