Problem 6: A Messy Boarding 1 Apr 2025

The problem

boarding

A plane has all of its 100 seats booked for the next flight. When the boarding starts, the first passenger to enter the plane is drunk, and sits on a random seat. After that, the remaining passengers enter the plane one by one, and sit on their seat if it’s free, or on a random one if their own place is occupied. What is the probability that the last passenger sits on the correct seat?

Solution