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?
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With one person there is a 365/365 chance they’ll have a new birthday
At two, there’s a 1/365 chance they’ll have the same birthday, or a 364/365 chance of a new one.
The third has a 2/365 chance of sharing a birthday with a previous person, or a 363/365 chance of having a new one.
Etc
To get the probability of someone sharing a birthday you multiply the odds of each person not matching a birthday together, and then subtract that from 1. So with 5 people you end up with 1 – [365•364•363•362•361 / 365⁵] to get 2.8% odds
The formula for calculating this out would be {1 – [ (365! /(365-n)!) / 365^n ] } where n is the number of people
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