Trivia

Subject:
Re: Friday Puzzler--100-seat plane

Larry Barrett
Suppose it is a 2 passenger plane.
A boards and could sit randomly in seat A (prob = 1/2) or seat B (prob = 1/2). So the probability that B sits in the correct seat is 1/2.

Now suppose it is a 3 passenger plane.
A boards and could sit randomly in seat A (prob = 1/3), seat B (prob = 1/3) or seat C (prob = 1/3).
If A sits in seat A, then both B and C will sit in the correct seats. If A sits in seat B, then the prob that B sits in seat A is 1/2 and then C will sit in the correct seat.
So the probability that C sits in the correct seat is 1/3 + 1/3 x 1/2 = 1/3 + 1/6 = 1/2.

It is an exercise for the reader to work out the probability for a 4 passenger plane.

...
So my guess is that in a 100 seat plane, the probability that the 100th passenger sits in the correct seat is 1/2.

Messages In This Thread

Friday Puzzler--100-seat plane
Re: Friday Puzzler--100-seat plane
Correct!
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