An old chestnut
goes like this:
How many people do you need to have together for the
probability that two of them have the same birthday to be at least 50%?
Usually these simplifying assumptions are used:
This is also written up in Birthday paradox (Warning: partial spoiler in link)
but it's not really a paradox
and the calculation is not described over there, only the answer, so I'm not using that node for this puzzle