Negative Binomial Probability
The negative binomial probability refers to the probability that a negative binomial experiment results in r - 1 successes after trial x - 1 and r successes after trial x.
Suppose a negative binomial experiment consists of x trials and results in rsuccesses. If the probability of success on an individual trial is P, then the negative binomial probability is:
\[b(x,r,p)= C_{r-1}^{x-1}\times P^r \times (1-p)^{x-r} \]
or
\[b(x,r,p)= \frac{(x-1)!}{(r-1) \times (x- r)!} \times p^r \times (1-p)^{x-r}\]
