# Negative binomial distribution

Keep tossing a coin until we have a total of $r$ heads (successes).

How likely to have $k$ tails (failures) before we stop?

$r$
$p$
$$p(k) = {k+r-1 \choose k}\cdot (1-p)^r p^k \\[16pt] \text{where r is the number of successes,}\\ \text{and p is the probability of success.}$$