Comment by pedrosbmartins
10 hours ago
> What is the probability that you are sharing the same birthday with people around you?
> What if I told you that in a room with only 23 people there’s already a 50% chance for two of them to have matching birthdays?
I guess it's the subject shift from _you_ to _any two people from a group_ that creates the surprise in the birthday paradox. You definitely need way more than 23 randomly sampled people to get to a high probability that _you_ specifically share a birthday with one of them, and the result does not contradict that notion.
Yeah, they should not have lead with subterfuge. It's still remarkable to many people (myself included) that a pool as small as 23 gives a 50% probability.
I think even given that premise, the "50% probability" is still a bit of a rug pull. The casual listener still believes the problem should address the 100% match.
A more honest approach is to plainly ask how many people have to be at a party to guarantee there are at least two people with the same birthday. To even the layman, the answer is 366 of course. Follow that though with, "And how many people will have had to arrive for there to be a 50% likelihood that two people at the party have the same birthday?"
To go from 366 to 23 I think is a surprise to many people. Because humans suck at probability, most people might instinctively assume half of 366 (183). So it becomes a surprise how low (less than two dozen!) it really is.
My own "drunk walk" to making sense of the small number: when two people are at the party, it is intuitive to me that there is 1 in 365 chance they will have the same birthday. As soon as a 3rd person arrives though there are two partygoers they might match so the odds have just doubled! :-) I understand though that the 4th person arriving does not double the odds but nonetheless increase the chances by 50%.
Suddenly I can now see a kind of asymptotic curve that, when we get to 366, will at last cross the threshold for 100% probability. But the asymptotic nature makes it clear to me that it will cross the 50% mark much sooner than would a linear growth. I am already convinced at this point that your 23 number is probably a pretty good one.
Sup-par phrasing is a subtle advantage of non-AI generated text. In the past, I would be put off by this bad phrasing and the typo ("requier") in the text, but these days, it's a signal that a human took the time to write this, which makes me happy to see.
..or is it "sub-par"?
I didn't even notice it at first!