Problem of the Week 1011

Musical Airplane Seats

Alice is at the front of a line of 100 people ready to board a 100-seat airplane. Bob is at the back of the line. Alice has lost her boarding pass, so she simply takes a random seat. Everyone else takes their proper seat if it is available, or takes a random empty seat if not. What is the probability that Bob gets to sit in his properly assigned seat?

Source: Mathematical Puzzles, A Connoisseur's Collection, by Peter Winkler (A K Peters).

© Copyright 2004 Stan Wagon. Reproduced with permission.