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Negative Binomial Probability Calculator

Find the probability of k failures before the rth success in independent trials.

Data stays on this deviceConvention explained below
Probability workspace
Probability workspace

Probabilities range from 0 to 1. Check whether the method gives cumulative or exact-count probability.

See the method

Set model parameters

Runs on your device

Your probability

Your result

Let’s calculate.

Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

  1. Enter required successes, failures before last success, success probability.
  2. Select Calculate to view the result.
  3. Check the method and assumptions below before using the result.

The method, explained

P(K=k)=C(k+r−1,k)p^r(1−p)^k.

A WORKED EXAMPLE

Using required successes = 3, failures before last success = 2, success probability = 0.5, the result is 0.1875. Change these example inputs to match your task; use the method above to check each step.

Understanding your result

Counts failures, not total trials. Trials are independent with constant success probability; very small probabilities may round to zero.

What to keep in mind

Counts failures, not total trials. Trials are independent with constant success probability; very small probabilities may round to zero. A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

Common questions

How do I use this negative binomial probability calculator?

Find the probability of k failures before the rth success in independent trials. Enter required successes, failures before last success, success probability. The starting example is editable; use values for the same system or project.

Which assumptions affect this result?

Counts failures, not total trials. Trials are independent with constant success probability; very small probabilities may round to zero.

Methodology maintained by ClarityKit. How these tools are built and checked.