The Waiting-Time Paradox

Why the bus always seems late

An interactive lesson with 6 steps, about 5 minutes: you predict, drag and solve, with instant feedback on every answer. It runs in your browser and needs JavaScript.

What you’ll learn

• Average wait $= \frac{\text{avg}(\text{gap}^2)}{2 \times \text{avg gap}}$, at least half the average gap.
• Uneven or random gaps make waits longer: you tend to land in long gaps.
• The inspection paradox: sampling by experience over-represents big cases.

Steps

1. Buses every 10 minutes
2. Bunched buses
3. Completely random buses
4. Busy gyms and full flights
5. Badly bunched
6. Class sizes