If you take a group of people born in a non leap year you would need 366 people for a 100% chance that someone shares a birthday but only 23 people for a 50% chance that somebody shares a birthday?
In: Mathematics
It’s a 50% that there is at least one match between 2 out of the 23 people. So for the first person there are 22 possible matches, for the second person 21 possible matches etc. the math works out to 50%.
There are plenty of excellent explanations here, so I’ll save you my explanation.
I will, however, share a fun fact about the birthday paradox. It is what’s called a *veridical paradox*.
A veridical paradox is a situation that produces a solution that seems entirely illogical, yet is objectively verifiable.
One of the more famous veridical paradoxes is the [Monty Hall Problem](https://en.m.wikipedia.org/wiki/Monty_Hall_problem). Upon first thought, it seems like a no-brainer that the answer is 50/50, but some simple math tells us that the answer is 2/3.
It’s not really a paradox. It’s just the way the math works out. It seems paradoxical bc human brains don’t naturally have a very intuitive sense of statistics.
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