Talk:Probabilistic method

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History

I removed the reference to the 1959 origins of the method because other examples came earlier, but I'm not sure when the actual origins are. Some sources sited Erdos' 1947 paper, others Szele's hamiltonian cycle result. Quite a few places seem to dodge the issue entirely (perhaps because the line between a "probabilistic" and a "counting" proof is so vague?

A striking example, dating back to 1909, is the normal number theorem, due to Émile Borel, that could be one of the first examples of the probabilistic method, providing the first proof of existence of normal numbers, with the help of the first version of the strong law of large numbers. I am not convinced that the terminology should be limited to results in combinatorics (perhaps to the favourite topics of Erdös, including number theory). Chassain (talk)12:59, 16 July 2011 (UTC)[reply]

Article Probabilistic proofs of non-probabilistic theorems

What is the connection of this article with this entitled "Probabilistic proofs of non-probabilistic theorems"? Pierre de Lyon (talk) 16:00, 2 May 2009 (UTC)[reply]

I would say this article is about probabilistic proofs in combinatorics, whereas the other article is a list of examples in other areas of mathematics. Charvest (talk) 19:05, 2 May 2009 (UTC)[reply]

Expected value

In the title and definition you write only about probability. However, both examples use Expected value . Is it accidentally? ru:МетаСкептик12 — Preceding unsigned comment added by МетаСкептик12 (talk • contribs) 10:41, 27 July 2012 (UTC)[reply]

Questions about second example

1. Why is the number of cycles of length i in the complete graph on n vertices is ${\frac {n!}{2\cdot i\cdot (n-i)!}}$ ? I thought it should be ${n \choose i}$ because each group of i vertices determines a different cycle.

2. You prove that two properties hold with positive probability, but how do you know that there is a graph that has both these properties? You cannot multiply the probabilities because the two properties are not necessarily independent!

--Erel Segal (talk) 09:58, 10 November 2014 (UTC)[reply]