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I'm working on a proof and to complete it I need to find a way to choose an $n$ such that $(1-a)^n < \epsilon$ for a fixed $a$ such that $\frac12 < a < 1$ and any small $\epsilon$. I'm trying to prove that a discrete probability space cannot contain an event $\mathcal A$ with probability at most $(1-a)^n$ since this clearly must go to 0. I'm just having a hard time finding an appropriate formula for $n$ to prove this goes to 0.

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    a = min(p, 1-p)2012-09-11
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    ?? If a=min(p,1-p), then a<1/2.2012-09-11

4 Answers 4