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MediumProbabilityAcceptance 55%
Drunk Passenger
Jane StreetCitadel
100 passengers board a full 100-seat plane. The first passenger lost their ticket and sits in a uniformly random seat. Each later passenger takes their own seat if free, else a random free seat. What is the probability the 100th passenger sits in their own seat?
Approach
Only seats 1 and 100 matter at the end.
Argue by symmetry between those two seats.
Answer
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