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? If you pick a fixed person (you) that would break the pigeonhole principle, I think.
I would think that saying "So if there are 23 people in the room there is a 50% chance any 2 of those people share the same birthday" is better.
Edit: I misunderstood, you're saying that other people are misunderstanding. My mistake!
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.
I would think that saying "So if there are 23 people in the room there is a 50% chance any 2 of those people share the same birthday" is better.
Edit: I misunderstood, you're saying that other people are misunderstanding. My mistake!