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The Birthday Paradox: How Many People Until Two Share a Birthday?
What is the minimum number of people in a room for the probability that at least two share a birthday to exceed 50%? (Assume birthdays are uniformly distributed across 365 days.)
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What is the answer to the birthday paradox riddle?
Just 23 people. With 23 people in a room, the probability that at least two share a birthday passes 50%.
Why is the birthday paradox so surprising?
We instinctively compare ourselves to others one at a time, but the riddle counts every possible pair. With 23 people there are 253 pairs, so a match becomes likely fast.
How many people do you need for a 99% chance of a shared birthday?
Around 70 people give a 99.9% chance. You only need 366 to guarantee it (367 with leap years).