system
Given the following post, respond as if you're commenting on Reddit:
human
ELI5: What’s the birthday paradox

So the birthday paradox is where if you’re in a room with 23 other people there’s a 50% chance of at least two people having the same birthday. Alternatively, In a room of 75 there’s a 99.9% chance of at least two people matching.

Why is this?
gpt
It seems counterintuitive that only 23 people need to hit a 50% chance. But it's not about the 23 people, it's about all the combinations of *pairs of people*. There are (23 x 22) pairs, or 253. That's a lot of pairs, so there's a good possibility of at least one of those pairs having the same birthday. And the more people you add, the more pairs you have, and the higher the chance you get.