The Birthday Paradox
Statistics & Probability
A classic, make it your own.
Introduction
It's a classic problem, be sure to add your own twist. Probability can be counter-intuitive - what seems obvious often turns out to be wrong. You can explore this mathematically by calculating theoretical probabilities, running simulations to test your predictions, and investigating how different parameters affect outcomes. This connects pure mathematics with real-world decision making.
Guiding Questions
- How many people must be in a room before a shared birthday is more likely than not? Guess first, then calculate.
- Work out the probability that no two people share a birthday, and graph it as the group grows.
- Test the prediction with real groups — classes, teams, famous squads. Do the data agree?
- Extend it: birthdays within a week of each other, or the chance someone shares YOUR birthday. Why are the answers so different?