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Fix $0 < p < 1$ and let $G$ be a random graph on elements $\mathbb{N}$ where for $n,m \in \mathbb{N}$, the probability that there is an edge between $n$ and $m$ will $p$. What is the probability (in terms of $p$) that $G$ will be connected?

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  • $\begingroup$ See this question: math.stackexchange.com/questions/584228/… Edit: nevermind I misread the question I wasn't thinking about infinite graphs. $\endgroup$ – Ben Oct 28 '15 at 0:54
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    $\begingroup$ Hint: you can actually prove that between every pair of distinct vertices there is (with probability 1) a path of length 2. $\endgroup$ – David Hackenger Oct 28 '15 at 1:01
  • $\begingroup$ @DavidHackenger Well that's that. If you type that into an answer I'll accept it. $\endgroup$ – JustAskin Oct 28 '15 at 1:08
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Hint: you can actually prove that between every pair of distinct vertices there is a path of length 2 (with probability 1).

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