Problem bank

Problem 277 of 333MediumProbabilityP277

The lost boarding pass

  1. 100 passengers board a plane with 100 assigned seats, one at a time in order. The first passenger has lost their boarding pass and sits in a seat chosen uniformly at random. Each later passenger sits in their own seat if it is free, and otherwise picks a free seat uniformly at random. What is the probability that the last passenger sits in their own seat?