MathDB
An absent-minded old lady

Source: Kvant Magazine No. 10 2021 M2673

March 9, 2023
combinatoricsprobabilityKvant

Problem Statement

There are nn{} passengers in the queue to board a nn{}-seat plane. The first one in the queue is an absent-minded old lady who, after boarding the plane, sits down at a randomly selected place. Each subsequent passenger sits in his seat if it is free, and in a random seat otherwise. How many passengers will be out of their seats on average?
Proposed by A. Zaslavsky