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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

Data and assumptions

Runs on your device

STATISTICAL RESULT

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

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.

Common questions

Which inputs does this calculation need?

Find the probability of exactly k successes in independent trials. Enter trials, successes, success probability. The filled example is editable and is not a saved personal record.

How should I interpret the result?

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.