100 passengers board a plane with 100 seats. The first passenger ignores their ticket and sits randomly. Each subsequent passenger sits in their assigned seat if available, or picks a random empty seat if not. What's the probability the last passenger sits in their assigned seat?

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Accepted Answer

50%. Either the first or last passenger's seat will be taken by the process. By symmetry, each is equally likely. If seat 1 is eventually occupied, passenger 100 gets their seat. If seat 100 is taken first, they don't.

Airplane Seats

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