Sunday Times Teaser 2904 – Catching Another Bus

by Michael Fletcher

Published May 20 2018 (link)

I want to catch a bus into town, and I arrive at the bus stop at a random time.

The number 12 bus runs every 12 minutes, the number 15 bus runs every 15 minutes and the number 20 bus runs every 20 minutes.

All the buses leave the bus stop at an exact number of minutes past the hour and no two buses leave at the same time. Interestingly, given the above information, the probability that I catch a number 12 bus is as small as it possibly could be.

What is the probability that I catch a number 12 bus?