negative binomial distribution
how many trials do you need to get r successes.
\begin{equation} P(X=n) = {{n-1} \choose {r-1}} p^{r} (1-p)^{n-r} \end{equation}
if the chance of individual success is p, what’s the probability that it takes n trials to get r successes.
\begin{equation} \mathbb{E}[x] = \frac{r}{p} \end{equation}
\begin{equation} Var[x] = r \frac{{1-p}}{r^{2}} \end{equation}