Binomial Probability Calculator | CountingMethods.com

Trial Parameters

Number of Trials (n)

Prob. of Success (p)

Number of Successes (k)

Exact Probability P(X = k)

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Likelihood of exactly k results

Expected Mean (μ)

Variance (σ²)

Std. Deviation (σ)

0% Cumulative P(X ≤ k) 100%

Cumulative Likelihood

Probability Mass Function (PMF)

The bar chart below represents the probability distribution for all possible successes. The highlighted bar corresponds to your input $k$.

Cumulative Distributions

Calculate to see cumulative ranges.

The Binomial Formula

The binomial distribution models the number of successes in $n$ independent trials, each with the same probability $p$.

                        P(X = k) = (n! / (k!(n-k)!)) * p^k * (1-p)^(n-k)
                    