No. 02
🎂Birthday Paradox
23 people, 50/50 odds of a shared birthday
The setup
- 1In a group of N people, what's the chance that at least two share a birthday?
- 2Most people guess you'd need a huge crowd to get even odds.
- 3In fact, just 23 people gives you a better-than-even chance.
🤔 Intuition says: There are 365 days, so surely you need ~180 people for a 50% chance?
📈 The probability curve
Exact probability of at least one shared birthday as the group grows. The dashed line marks 50% — drag the slider and watch where 23 people land.
🧪 Run the experiment
Why it's a paradox
You're not matching one specific person — you're matching any pair in the group.
A group of 23 people contains 253 distinct pairs (23 × 22 / 2), and each pair is a chance for a collision.
The probability of no shared birthday shrinks fast as pairs pile up, so the match probability climbs much faster than intuition expects.
💡 Key insight: Coincidence scales with the number of pairs, not the number of people.
Further reading on Wikipedia →