What is the Birthday Paradox?
Contrary to intuition, the famous probability paradox states that in a group of just 23 people, the chance that two of them share a birthday is already over 50%. People tend to underestimate the "chance of a match out of 365 days," but the number of possible "pairs" grows much faster than the number of people, so the probability ends up being far higher than expected.
Why is the probability so high?
With 23 people, the number of possible pairs is 23 Γ 22 Γ· 2 = 253. Since there are 253 chances for a match, even though each individual pair has a low chance of matching, the overall probability of at least one match climbs quickly. With 70 people, the probability exceeds 99.9%.
Frequently Asked Questions
Does this calculation account for leap years?
No, to keep the calculation simple it assumes a 365-day year with an equal probability of being born on any date. In reality, birth rates vary slightly by season, so the actual probability may differ a little.
Is this different from "the probability someone shares my birthday"?
Yes, it's different. The probability of finding someone who shares your specific birthday is much lower. This calculator finds the probability that any two people in the group share a birthday.