There is a mildly related math puzzle I learned at some point in high school (iirc):
someone comes to a subway station at (uniform) random times between 6p and 8p; he notices that the first train he observes arriving at the same station is 3 times more often inbound than outbound. He also knows that time intervals between the trains going in the opposite directions are fixed and equal — say, always 6 minutes, so the only random event here is when this person arrives at the platform. Explain how this is possible.
The outbound ones are scheduled a minute and a half after the inbound. (For neat integers, should have been twice as often, or 8 minutes between them.)
But the bigger question: What's the difference between "an inbound train" and "an outbound train"? Aren't almost all trains usually both inbound and outbound? First they arrive at a station, then they go on to the next. Or even at a "terminus"-type station; first they arrive at the terminus, then they go back in the other direction. How does he decide whether a train is an inbound or an outbound one, while it is standing still?
someone comes to a subway station at (uniform) random times between 6p and 8p; he notices that the first train he observes arriving at the same station is 3 times more often inbound than outbound. He also knows that time intervals between the trains going in the opposite directions are fixed and equal — say, always 6 minutes, so the only random event here is when this person arrives at the platform. Explain how this is possible.