# Boarding Pass

You’re one of a hundred people standing in line to get onto an airplane that has 100 seats. The first person to walk onto the plane drops his boarding pass and takes a seat at random. What are the chances that you get to sit in your assigned seat? A) one out of two, B) one out of ten, C) two out of 50, which happens to be one out 25, D) one out of 100, and E, zero. Please explain your answer.

### 2 guesses to Boarding Pass

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• Paul

One out of two, since everyone else will find their assigned seat except the guy that was assigned the seat the first person took. That guy could be you or a another guy that will either take your assigned seat or take the first person’s assigned seat. So fifty-fifty, either you’ll sit in your assigned seat or that other guy will.

• You’re correct, Paul!

Now our guy with the lost boarding pass, he could by dumb luck wind up in his assigned seat, right? But what’s more likely is that he takes someone else’s seat (it’s much more likely).

Now, here’s the counterintuitive part. There are only two seats that count, my seat and his seat. All the other seats don’t make a difference. Whoever gets on the plane subsequent to him, those people are going to take some seat or another. Nothing matters until either my seat gets taken or his seat gets taken. If my seat gets taken by some displaced passenger, then I have zero chance of getting my seat. If his seat gets taken by some displaced passenger then every other passenger who walks onto the plane including me, will have his assigned seat. And how often does that happen? One time out of two. Half the time my seat’s going to get taken by some displaced passenger, and half the time his seat is going to get taken by a displaced passenger. So your chances are A) one out of two.

Congrats! You’re today’s winner.