Talk:Birthday problem

logarithms and combinations

I just noticed this, which I don't see in the article: ${\frac {\log(1/2)}{\log(364.25/365.25)}}\approx 252.83\approx {\binom {23}{2}}$ —Tamfang (talk) 18:01, 28 March 2024 (UTC)

So what? --Macrakis (talk) 20:37, 28 March 2024 (UTC)

364.25/365.25 is the probability that a given pair do not share a birthday. 253 is the number of pairs among 23 people. I never knew before why the threshold number is 23. —Tamfang (talk) 06:15, 29 March 2024 (UTC)

So you're saying that this is more than a coincidence? --Macrakis (talk) 15:45, 29 March 2024 (UTC)

Much closer, but equally meaningless: 365*log(2) = 252.999. --Macrakis (talk) 21:17, 28 March 2024 (UTC)

Or to put that another way, 23 is the smallest integer n such that $({\frac {364.25}{365.25}})^{\binom {n}{2}}\leq {\frac {1}{2}}$. —Tamfang (talk) 00:03, 30 March 2024 (UTC)

OK, I think I'm beginning to follow you here. Small detail: article says that leap years aren't taken into account, so it should be 364/365. --Macrakis (talk) 15:08, 1 April 2024 (UTC)

Is partition problem relevant to this article?

To me, the partition problem at the bottom of the article does not seem sufficiently related to the birthday problem. Is the motivation behind the inclusion that both problems have the "answer" 23? Zaspagety (talk) 13:59, 9 April 2024 (UTC)

I'm inclined to agree with you: although the content has been in the article a very long time, it doesn't seem actually relevant to the topic of this article except in a hand-wavy way. The unique citation does not mention the birthday problem. --JBL (talk) 18:03, 9 April 2024 (UTC)

The probability of a pair is almost the same as the error function and/or arctangent

In fact, im inclined to believe that as the number of days goes to infinity, the function becomes more like erf / atan. I knwow this sounds dumb, but has someone done written a math paper on this??? Qsimanelix (talk) 19:29, 30 August 2024 (UTC)