Solution
Birthday Paradox
Show the problem again
Assuming birthdays are uniformly distributed across 365 days and ignoring leap years, what is the minimum number of people needed in a room such that the probability of at least two sharing a birthday exceeds 50%?
Worked solution
The answer is 23. The probability that all n people have distinct birthdays is 365/365 × 364/365 × ... × (365−n+1)/365. For n=22 this is about 52.4% (under 50% shared), for n=23 it drops to 49.3%, meaning a shared birthday becomes more likely than not.
Source: Classic result popularised by Richard von Mises (1939); standard in probability texts. Statement written for AxiomIQ.