Free Binomial Probability Calculator
Probability of exactly k successes in n trials.
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Result
P(X = 4)
20.5078%
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Short answer
Probability of exactly k successes in n trials.
What is the Binomial Probability Calculator?
Probability of exactly k successes in n trials.
How does the Binomial Probability Calculator work?
Enter the inputs above and read the result.
Formula
Variables
C(n,k)Combinations of n choose k
Explanation
The binomial distribution models the count of successes in a fixed number of independent yes/no trials.
Examples
Applications
Advantages
Limitations
Common mistakes
Tips
Related concepts
The Binomial Probability Calculator sits inside the Math Calculators hub, in the statistics & probability cluster. Describing data and quantifying uncertainty. Understanding the terms below makes the output easier to interpret and easier to compare against neighbouring measures.
Practical use cases and industry applications
Understanding Binomial Probability
Probability of exactly k successes in n trials. Within math calculators, binomial probability belongs to the statistics & probability cluster, where it shares terminology and assumptions with closely related tools.
Learning how binomial probability is calculated
The binomial distribution models the count of successes in a fixed number of independent yes/no trials. Working through the variables one at a time — C(n,k) — makes the result reproducible by hand and easier to sanity-check.
Using binomial probability to make a decision
Because outputs depend on the assumptions you enter, run more than one scenario before committing to a figure.
How binomial probability compares with related measures
distribution, dispersion, significance, sample all describe adjacent aspects of statistics & probability. Comparing this calculator's output against those measures — using the related tools listed on this page — prevents a single metric from being read in isolation.
Frequently asked questions
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