Why I hate an empty bus stop

Rafael Prieto Curiel, in the mathematics magazine Chalkdust, does some rough calculations about waiting for a bus:


“Let’s measure how much time I expect to wait for the next bus to arrive as I observe more or fewer passengers in the stop…. If I find zero passengers at the bus stop, 99% of the time I will have to wait more than 15 minutes for the next bus. However, if I arrive at the bus stop and I find 25 or more passengers, then 99% of the time I have to wait less than 6 minutes for the next bus! Rarely, very rarely, I will find an empty stop with the next bus nearby, therefore, I prefer a crowded stop and then I just cross my fingers hoping that the bus is not too crowded too…. Next time I arrive at a bus stop that doesn’t have the “next bus in X minutes” I can simply count the number of passengers waiting at the stop and obtain a fairly good estimate of my expected waiting time.”