What’s the birthday paradox

Question

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?

In: 134

Answer 1

essentially its not a 50% chance that 1 person in particular shares a birthday, its the chance any 2 people have a matching birthday, so you have 22+21+20+19…+2+1 = 246 chances.