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# Chance of getting his seat.

## Question

One hundred people line up to board an airplane. Each has a boarding pass with assigned seat. However, the first person to board has lost his boarding pass and takes a random seat. After that, each person takes the assigned seat if it is unoccupied, and one of unoccupied seats at random otherwise. What is the probability that the last person to board gets to sit in his assigned seat?

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Spoiler

Assume that passengers 2-98 ask (if necessary) the forgetful passenger to leave his seat and THIS passenger then choses a seat at random.

When the last passenger boards, 98 are correctly seated. The forgetful passenger occupies either his own seat or that of the 100th passenger.

So p=50%.

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3 hours ago, harey said:
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Assume that passengers 2-98 ask (if necessary) the forgetful passenger to leave his seat and THIS passenger then choses a seat at random.

When the last passenger boards, 98 are correctly seated. The forgetful passenger occupies either his own seat or that of the 100th passenger.

So p=50%.

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