The Waiting-Time Paradox

Abstract

Suppose that you are going to school and arrive at a bus stop. How long do you have to wait before the next bus arrives? Surprisingly, it is longer—possibly much longer—than what you might guess from looking at a bus schedule. This phenomenon, which is called the waiting-time paradox, has a purely mathematical origin. In this article, we explore the waiting-time paradox, explain why it occurs, and discuss some of its implications (beyond the possibility of being late for school).