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Statistics

Binomial Probability Calculator

Find the probability of exactly k successes in independent trials.

Data stays on this deviceConvention explained below
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Check the dataset and sample convention before interpreting results.

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Use the Calculate button to see your result.

Review the method below for assumptions and conventions.

How to use this tool

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

Input reference and sample values

Use the units and choices shown for each field. Sample values are provided for practice, not as recommendations.

InputFormat and unitsSample
TrialsWhole numbers only. Zero or positive. Maximum: 1000.10
SuccessesWhole numbers only. Zero or positive. Maximum: 1000.3
Success probabilityNumeric value. Zero or positive. Maximum: 1.0.5

Result for these sample inputs

0.1171875 probability

Select Try the example in the form to load these values and calculate them again. This replaces the current form inputs. Compare the result with the method and worked explanation below.

The method, explained

P(X = k) = C(n,k) p^k (1 − p)^(n − k).

A WORKED EXAMPLE

Using trials = 10, successes = 3, success probability = 0.5, the result is 0.1171875 probability. Change these example inputs to match your task; use the method above to check each step.

What to keep in mind

A descriptive or probability calculation under the stated assumptions. Check the sample design and model before interpreting results.

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