ELi5: what’s the birthday paradox ? And is its mathematical basics a correct proof?
In: Mathematics
The Birthday Paradox asks: “How many people do you need to put in a room before two of them probably have the same birthday?”.
A lot of people immediately say 365, thinking “there are 365 days, so if we put in 365 people, then we’ll probably find two that share a birthday”. The “paradox” is that actual answer is much smaller, though!
The true answer is 23 – with only 23 people in the room, two of them probably share a birthday. The trick is that Person 1 checks their birthday with Person 2, and Person 3, and Person 4, etc…and then Person 2 is *also* checking their birthday with Person 3, and Person 4, etc…and the number of people checking birthdays goes **way** up when you realize that every is checking *every possible combination of birthdays* against everyone else in the room.
It turns out that with 23 people, the odds of two of them sharing a birthday edge up above 50%, which is “probably” when it comes to statistics.
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