Negative binomial distribution

In probability theory and statistics, the negative binomial distribution, also called a Pascal distribution, is a discrete probability distribution that models the number of failures in a sequence of independent and identically distributed Bernoulli trials before a specified/constant/fixed number of successes r {\displaystyle r} occur. (Sometimes the roles are swapped: the number of failures is fixed and the number of successes is modeled.) For example, we can define rolling a 6 on some dice as a success, and rolling any other number as a failure, and ask how many failure rolls will occur before we see the third success ( r = 3 {\displaystyle r=3} ).

Source: Wikipedia — Negative binomial distribution (CC BY-SA 4.0)