Birthday Paradox

🎂 The Birthday Paradox

In a group of just 23 people, the chance that two share a birthday is about 50.7% — surprisingly high. Pick a group size and explore this famous mathematical fact.

Chance at least two of 23 people share a birthday

50.7%

About 50.7% for 23 people. Crossing 50% at just 23 is why it's called a "paradox".

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Probability by group size

5 people 2.7%
10 people 11.7%
23 people 50.7%
30 people 70.6%
41 people 90.3%
50 people 97.0%
70 people 99.9%

What is the Birthday Paradox?

It is the well-known fact that in a group of 23 people, the probability that two of them share a birthday exceeds 50%. Because we count every possible pair (not matches to one specific person), the number of pairs grows fast, so the probability climbs quickly. It is computed exactly as 1 − (365/365 × 364/365 × 363/365 × …).

A mathematical fact assuming 365 equally likely days (in reality, leap day Feb 29 and birth seasonality shift it slightly). Not fortune-telling. About our data