Exact model

A shared birthday in a room of 30

Probability:
70.6%
Odds:
2.4 to 1
dBan
+3.8 dBan

In a room of 30 people, a shared birthday is already more likely than not: it appears in about 71 in 100 modelled groups.

Calculation

p = 1 − ∏ₖ₌₀²⁹ (365 − k) / 365 ≈ 0.70631624

Assumptions

Birthdays are independent and equally spread over 365 dates. Leap days are ignored.

Sources

  1. Uniform 365-day birthday model