What is the Probability of the Outcomes of a “Repeat Until Success” Experiment?

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)?

• Is this not a geometric distribution? – Parcly Taxel Oct 10 '16 at 5:08
• Yes, it is exactly that. Post an answer with a link to a page describing the geometric distribution and receive your reward. – Sean Lake Oct 10 '16 at 5:09

The probabilities are given by the geometric distribution: $$\mathsf P(n\text{ failures before success})=(1-p)^np$$