The Quant 7510 / 75
MediumProbability
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.
Sign in to reveal the full worked solution, check your answer instantly, and track your progress with spaced-repetition review.
Related problems
Coin Toss — Two HeadsEasyBirthday ProblemMediumBroken Stick TriangleMediumHat CheckMediumRussian Roulette — Spin?MediumExpected Max of Two UniformsMedium
More in Probability.