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Calculation Machine

Negative Binomial Distribution Calculator

Probability of the rth success on the nth trial.

Reviewed by James Whitfield · How we check our maths

Your values

ⓘ Live results

Results
P(N = n)
12.4416%
Expected trials for r successes
7.5
Parameters
r=3, p=0.4, n=7

Quick answer

The negative binomial distribution gives the probability of needing exactly n trials to get r successes, each trial succeeding with probability p.

The formula

P(N=n) = C(n-1, r-1) p^r (1-p)^(n-r)

Worked example

Worked example

Using the values the calculator loads with.

Inputs

  • Target number of successes r3
  • Success probability p0.4
  • Trial number n7

Result

  • P(N = n)12.4416%
  • Expected trials for r successes7.5
  • Parametersr=3, p=0.4, n=7

How to use the Negative Binomial Distribution Calculator

  1. 1Enter the target number of successes r.
  2. 2Enter the per-trial success probability p.
  3. 3Enter the trial number n on which the rth success should occur.

Frequently asked questions

How is this different from binomial?

Binomial fixes the number of trials and counts successes; negative binomial fixes the number of successes and finds the trial count.

What is the expected number of trials?

On average, r/p trials are needed to reach r successes.

About this calculator