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Birthday problem was a Natural sciences good articles nominee, but did not meet the good article criteria at the time. There may be suggestions below for improving the article. Once these issues have been addressed, the article can be renominated. Editors may also seek a reassessment of the decision if they believe there was a mistake.

Article milestones
Date	Process	Result
October 1, 2007	Good article nominee	Not listed

Mathematics B‑class Low‑priority

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Statistics B‑class Low‑importance

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Is 100% linkable to Almost surely

Despite its name almost, the article states that it is a case of probability one unless that too is wrong. Is there another article which describes this case that I'm missing? Ugog Nizdast (talk) 15:25, 21 November 2016 (UTC)[reply]

"Probability 1" and "guaranteed always to occur" are not the same thing, as explained in that article. For example, in choosing a real number in the interval [0, 1] uniformly at random, the probability of getting an irrational number is 1, but there are choosable numbers that are not irrational. The sentence you edited is not like this: given 367 selections from a set of size 366, it is not possible to make a set of choices with no repetitions. This is much more straightforward and less subtle than "with probability 1." --JBL (talk) 15:44, 21 November 2016 (UTC)[reply]

I think if I've fairly understood this then, as you said, "it is not possible" is different from "100% probability"...why does the lead then mention "...the probability reaches 100%..."? Shouldn't it just say something like guaranteed to always occur or other cases are simply not possible at the point onwards? Thanks for humouring me btw, Ugog Nizdast (talk) 11:48, 28 November 2016 (UTC)[reply]

Right, "the negation cannot happen" is stronger than "the probability of occurring is 100%" in general (and the latter is what is called "almost surely"). There is one major reason for the present wording, which is that the entire discussion is phrased in terms of probability, so it is natural to continue using that language. Also, in this context (that of a finite probability space), the two notions (100% probability and must happen) actually do coincide (so in finite probability we don't need the more sophisticated notion of almost sureness). --JBL (talk) 13:46, 28 November 2016 (UTC)[reply]

Error in the justification of the calculation

In the justification of the main calculation, the text describes the events as independent. But it seems to me that they are not actually independent, since the probability that person n has a birthday different from the earlier people depends on whether the earlier people have all different birthdays or not. That is, in the case there were already some common birthdays, the probability would rise slightly for person n to avoid an overlap. So the justification of the calculation in terms of independent events seems to me to be incorrect. It would be correct, instead, to be talking about conditional probability, that is, the probability that person n has a different birthday, given that the earlier people all have different birthdays. The final numbers would be the same as currently, with this correct way of justifying them. JoelDavid (talk) 01:44, 6 December 2016 (UTC)[reply]

Indeed, as written it is nonsense. --JBL (talk) 00:08, 12 December 2016 (UTC)[reply]

Partition Problem

The Partition Problem section makes a claim about 23 that is not supported directly by the one reference given in this section. I added a citation needed tag to the 23 claim, but the entire explanatory paragraph (that begins "The reason is that..") is very weak and reads like poorly written original research. Anybody interested in finding a decent reference for the main claim of this section? That would be awesome. Doctormatt (talk) 05:42, 10 December 2016 (UTC)[reply]

The Birthday Problem and the Schnabel Census

After having read the original paper by Zoe Schnabel (reference 10 in the article) on her now-called Schabel census, I think the claim of the article, that

The theory behind the birthday problem was used by Zoe Schnabel[10] under the name of capture-recapture statistics to estimate the size of fish population in lakes.

is essentially not correct. There is an ambiguity in the phrase ``theory behind the birthday problem, but, as the Wikipedia article on mark-and-recapture shows, the Schnabel census is better seen as an extension of the Lincoln-Petersen estimator than as something which drops out of the Birthday Problem in some unspecified way.

At the very least, if the claim is going to be made, the assertion should be developed as a subsection and the algebraic connection shown. Otherwise, I recommend either deleting the comment, or saying that the methods are related to the major articles on mark-and-recapture or the Lincoln index.

empirical_bayesian@ieee.org

This user is a member of WikiProject Statistics.

19:44, 23 June 2017 (UTC)

@@ Line 52: / Line 52: @@
 After having read the original paper by Zoe Schnabel (reference 10 in the article) on her now-called ''Schabel census'', I think the claim of the article, that
-{{The theory behind the birthday problem was used by Zoe Schnabel[10] under the name of capture-recapture statistics to estimate the size of fish population in lakes.}}
+<blockquote>The theory behind the birthday problem was used by Zoe Schnabel[10] under the name of capture-recapture statistics to estimate the size of fish population in lakes.</blockquote>
 is essentially not correct. There is an ambiguity in the phrase ``theory behind the birthday problem'', but, [[Mark_and_recapture#More_than_two_visits|as the Wikipedia article on mark-and-recapture shows]], the Schnabel census is better seen as an extension of the [[Lincoln_index|Lincoln-Petersen estimator]] than as something which drops out of the Birthday Problem in some unspecified way.