It is known that for choosing 2 people out of n with birthdays A,B the probability that A=B is $\frac{1}{365}$. In this case we have replacement which means that we may choose the same person twice. A and B are of course independent. What I need to understand is the case where we choose two different people without replacement. Let's assume that X,Y are their birthdays, then Y is dependent of X (right?). What is the probability that X=Y?
2026-02-23 08:22:49.1771834969
Same birthday for two people with and without replacement
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