Puzzles
Buses come every 10 minutes on average. Why does your wait always feel longer?
If buses arrive at a stop every 10 minutes on average but at irregular intervals, common sense says a random arrival should wait 5 minutes on average — half the gap. Why is the real average wait actually closer to the full 10 minutes, not half?
Reveal the answer
Because you're more likely to arrive during a long gap between buses than a short one — the long gaps simply take up more of the clock. This 'inspection paradox' means randomly sampling a moment in time oversamples long intervals, so your expected wait equals close to the full average interval, not half, unless the buses run on a perfectly fixed schedule.