You're misquoting or misunderstanding. The comment to which you are replying said:
The paradoxy bits of the problem are the things that
people find confusing. "Only 23?!" or "So if there are
23 people in a room there's a 50% chance that one of
them will share a birthday with me?"
In that comment he is saying that people mis-understand the question, and assume that it means that once there are 23 people in the room, then there's a 50:50 chance they will share a birthday with them specifically.
And that's exactly the wrong question, as you point out. So when you say:
Is "So if there are 23 people in a room there's a 50% chance
that one of them will share a birthday with me?" correct?
No, that's not correct, but it is what people think they hear, and it's that confusion that makes this whole thing sometimes called a paradox.
So let's be clear:
If you're in a room with 22 other people, the chance
that one of them shares a birthday specifically with
you is nowhere near 50%
However, the chance that among the 23 people in the
room there is, somewhere, a shared birthday, is indeed
slightly greater than 50%
And my experience is that it really doesn't matter how carefully you word this, some people simply will not understand it.
And that's exactly the wrong question, as you point out. So when you say:
No, that's not correct, but it is what people think they hear, and it's that confusion that makes this whole thing sometimes called a paradox.So let's be clear:
And my experience is that it really doesn't matter how carefully you word this, some people simply will not understand it.