To explain why our intuitions lead us astray here, we’re used to thinking about coincidences like this from our own perspective, or at least from a single person’s perspective. When *you* walk into that room and ask a random person what their birthday is, yeah, chances are it’s not going to be the same as yours. Neither is the next person you ask, or the next.
But the question isn’t about any one specific person sharing your birthday, it’s about *any pair* of people. And even with only 23 people in the room, there are a lot of different pairs of people there – 253 of them. A 1 in 365 chance is small, but getting 253 shots at it…
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