why in a room with 23 people there’s a good chance 2 of them share a birthday
In: Mathematics
Let’s start with 2 people. Person one has a birthday on one day. So for person 2 to not have the same birthday it is 364/365.
.997% chance to not match. .003 chance to match
Now if we add a third person there is a 363/365 chance of them NOT lining up with the first two. So we multiple 364/365 and 363/365.
.991% chance to not match. .009 chance to match
For the fourth person we do the same. Multiplying the previous chance of there not being any matches by 362/365.
.983% chance to not match. .017 chance to match
As we add more people the fraction we are multiplying by gets smaller and we’ve multiplied it more times so the percentage of not having a match gets high fairly quickly.
Ninja edit:
Here is the formula using factorials ( 3! = 3 * 2 * 1)
(364!/(364-n)!)/365^n
In this n is the number of people. And the result is the chance that they will NOT share the same birthday. At 23 the chance to not share is 46% so the chance they share a birthday is 54%
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