Binomial Distribution Calculator
Find the probability of exactly or at most k successes in n trials. The result updates as you type, with the working underneath so you can check it.
Your details
Result
P(X = 3)
0.117188
- P(X ≤ k)
- 0.171875
- P(X ≥ k)
- 0.945312
- Mean (np)
- 5
- Std deviation
- 1.58114
Good to know: P(X = k) = C(n,k) pᵏ (1−p)ⁿ⁻ᵏ
About this tool
Formula
P(X = k) = C(n,k) pᵏ (1−p)ⁿ⁻ᵏ
Questions people ask
When do I use a binomial distribution?
For a fixed number of independent trials with two outcomes and the same success probability each time, such as coin flips.
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How we calculate this
We use the standard published formula or definition for this calculation, and we show the working so you can check it.
Spotted a mistake? Tell us and we'll check it. How we check our calculators