I'm fixing a software defect that occurs 1 in n test runs. If I want to know that the probability of it being fixed is >= p for some 0 <= p < 1, how many times, m, do I need to run the test successfully (without the defect occurring)?

closed as off topic by Gerald Edgar, Harald HancheOlsen, Steve Huntsman, Noah Snyder, Douglas Zare May 7 '10 at 19:19
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According to my statistics final which I took yesterday, the answer should be 


I guess $m>\log(1p)/\log(11/n)$ works since the probability of a faulty system running $m$ times without defect is $(11/n)^m$ and this should be smaller than $1p$. This seems to be a homework type question (and moreover an easy one) rather than a MOquestion. 


If your problem was a little bit more difficult (rolandbacher already provided an easy, precise and correct solution) and your $n$ is big, you can also approximate the binomial distribution by a Poisson distribution. Repeating the test $m$ times gives then the parameter $\lambda = \frac{m}{n}$ and your goal is that $m$ is big enough that $e^{\lambda}\ge 1p$. So $m \ge n\ln(1p)$. The approximation by the Poisson distribution is pretty good, for $n = 500$ and $p = 0.99$ it yields $m > 2302.585$ instead of the correct $m > 2300.28$ given by rolandbacher's formula. 

