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I have an procedure that is known to be a Bernoulli trial with two possible outcomes. Let the probability of the outcome labeled success be $p$. If the experiment is to repeat the procedure until a successful outcome is acquired, what is the probability of the different outcomes (all of which are described by $n$ fails followed by $1$ success)?

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    $\begingroup$ Is this not a geometric distribution? $\endgroup$ – Parcly Taxel Oct 10 '16 at 5:08
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    $\begingroup$ Yes, it is exactly that. Post an answer with a link to a page describing the geometric distribution and receive your reward. $\endgroup$ – Sean Lake Oct 10 '16 at 5:09
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The probabilities are given by the geometric distribution: $$\mathsf P(n\text{ failures before success})=(1-p)^np$$

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