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?
In: 134
**The Math:**
(364/365)^253 = 0.4995
**The Explanation:**
253 unique pairs come from 23 people.
364/365 chance they *dont* share a birthday.
Like a coin flip, each time we check we are actually multiplying the odds exponentially. With a coin flip the probability is 0.5, but here it is 364/365.
So the result, 0.4995, is the odds they don’t share a birthday. That means the odds they *do* share a birthday is 0.5005, or 50.05%
It is a veridical paradox, which just means it defies our brains’ natural assumptions. It isn’t a paradox in the traditional sense.
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