Statistics calculator

Binomial Probability Calculator

Calculate exact and at-least binomial probability from trials, successes, and success probability.

FormulaP(X = k) = nCk p^k (1 - p)^(n-k)

Formula

Binomial probability

This assumes independent trials with the same success probability.

P(X = k) = nCk p^k (1 - p)^(n-k)

10 trials, 3 successes, and 40% success probability can be evaluated exactly.

FAQ6 common questions for this calculator.

FAQs

What does at least k mean?+

It sums probabilities from k successes through all successes.

Can trial count be large?+

The calculator caps inputs to keep factorial math practical.

How does the Binomial Probability Calculator calculate the result?+

For the Binomial Probability Calculator, it uses the Binomial probability: P(X = k) = nCk p^k (1 - p)^(n-k). 10 trials, 3 successes, and 40% success probability can be evaluated exactly.

What information do I need to use the Binomial Probability Calculator?+

For the Binomial Probability Calculator, enter trials, successes, and success probability. Keep the units consistent with the calculator fields and compare your setup with the worked example on the page.

How accurate is the Binomial Probability Calculator?+

Binomial Probability Calculator calculates the selected statistic from the sample values provided. It uses the Binomial probability, but missing data, outliers, sample bias, and distribution assumptions can affect what the result means.

What should I check before using the Binomial Probability Calculator result?+

For the Binomial Probability Calculator, check trials, successes, and success probability, sample definition, missing values, outliers, and rounding precision. A statistic can be numerically correct but still describe a weak sample.

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Statistics guide

How to use the Binomial Probability Calculator

Calculate exact and at-least binomial probability from trials, successes, and success probability. The page also explains the binomial probability and shows a practical example: 10 trials, 3 successes, and 40% success probability can be evaluated exactly.

  1. 1

    Enter your details

    Enter trials, successes, and success probability, then complete any other fields shown in the calculator.

  2. 2

    Check the calculation

    Review the result alongside the binomial probability: P(X = k) = nCk p^k (1 - p)^(n-k).

  3. 3

    Compare scenarios

    Change one or more inputs to see how they affect the binomial Probability Calculator result before you use the estimate.