Talk:Birthday problem

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logarithms and combinations

I just noticed this, which I don't see in the article: $\frac{\log (1/2)}{\log (364.25/365.25)}\approx 252.83\approx (\genfrac{}{}{0ex}{}{23}{2})$ —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 $(\frac{364.25}{365.25}{)}^{(\genfrac{}{}{0ex}{}{n}{2})}\le \frac{1}{2}$. —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)

Taking that further, the approximation n >= 0,5 + sqrt(0,25 + 2 * ln(2) * 365) mentioned in the article could then be improved by writing it as n >= 0,5 + sqrt(0,25 + 2 * ln(2) / ln (365/364)) Roelgrif (talk) 02:16, 11 January 2025 (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)

BS

There are no examples here of real life tests. Like going into a classroom or office and asking people. If this is just a BS numbers game it should be made clear at the start. 2A00:23C8:E414:1F01:6D85:5817:D045:A7F3 (talk) 23:16, 10 April 2025 (UTC)