[vageli]

> Assuming a uniform distribution, the probability is 1/365 for any person#. Those probabilities add up linearly if the people are guaranteed to have different birthdays (union/OR). Otherwise the probability of NOT having someone with the same birthday goes down exponentially as a an exponential power of the fraction 364/365 (intersection of complement/AND NOT)

Why would we assume a uniform distribution of birthdays? For example, birthdays occurring on the 31st of a month are probably less likely to occur on average given that every month does not have 31 days. This is just one example and doesn't even go into seasonality of conception cycles.

[EGreg]

To simplify. Mathematical models don’t perfectly capture all the details usually.