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Birthday paradox group probability

modified2026-07-21statusfinished

Probability that at least two people in a group share a birthday.

[10.4] Governing equation

$$P(\text{match})=1-\prod_{k=0}^{n-1}\left(1-\frac{k}{365}\right)$$

Source: 1728 Software Systems.

50% n=23 n →
FIG. 01 — match probability rises sharply, crossing 50% at n = 23