In probability theory, the birthday problem asks for the probability that, in a set of n randomly chosen people, at least two will share the same birthday. The birthday paradox is the counterintuitive fact that only 23 people are needed for that probability to exceed 50%.



What made me understand this was realizing that it meant any two people. The first time I heard this I was thinking that if I was in a group of 70 or 80 people, there was almost a 100% chance of someone having the same birthday as me. But it’s not comparing to an individual, it’s comparing all of the pairs. I hope that makes sense