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# Negative Binomial Distribution Calculator

Aa free online tool for calculating probabilities of events following negative binomial distribution.
Negative binomial distribution describes the probability that the x-th independent trial will be the k-th success provided each success has the same probability p:
 P(X=x) = ( x-1 k-1 ) (1-p)x-k pk
Alternatively, the distribution describes the probability of the next independent trial being the k-th success after a fixed number r of failures have occurred:
 P(k, r) = ( k+r-1 k-1 ) (1-p)r pk

x>0, k>0, x≥k, r≥0, 0<p<1; x = k + r

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Calculate

## Calculator

Probability of success in one trial:p =

Number of successes:k =

Calculate the probability that the x-th trial will be the k-th success:
x = , or alternatively, set the number of failures:r =
Calculate the total probability of all values x from the interval x1 - x2:
x1 = x2 =

P(X = x):

P(X ≤ x):

P(X ≥ x):

Mean: