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
The reason the number is so low compared to what one might expect is because the instinctive way people think of this is usually “How many people would I need to have in a room before one of them had my birthday?” even if they don’t neccesarily think those exact words in their head. That’s a different question. What we want to know is how likely is it that ANY two people match birthdays.
So when you have two people in a room there’s two people that both have a 1/365 shot. With three people you have three people who each have a 2/365 shot and so on. So with 23 people each of them has a 22/365 shot. That ends up with 254 unique combinations.
254 tries at a 1/365 suddenly doesn’t seem like such long odds
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