I got into a discussion with a friend about this simple question:
Provided that I went to a class with $N$ people, where everyone was born the same year in the same city where there are $K$ hospitals, what's the probability that someone was born in the same hospital and in the same day as me?
My approach would be as follows:
$\left( 1- \left(\frac{364}{365} \right)^N \right) \cdot \left(1-\left(\frac{K-1}{K} \right)^N \right)$
But I'm not really sure that this is the correct answer :)