Binomial Distribution
Statistics & ProbabilityCalculate exact Binomial probability mass P(X = k), cumulative probability P(X ≤ k), mean, and variance for n independent Bernoulli trials with success probability p.
P(X ≤ 10) = 0.5881 · P(X ≥ 10) = 0.5881
About this calculator
The Binomial distribution models discrete experiments with a fixed number of independent trials (n), where each trial has only two outcomes (success or failure) and a constant probability of success (p).
This calculator evaluates exact probabilities P(X = k), cumulative probabilities P(X ≤ k) and P(X ≥ k), and graphs the probability mass distribution alongside expected mean (μ = np) and standard deviation (σ = √(np(1-p))).
How It Works & Formula
P(X = k) = C(n, k) × pᵏ × (1 - p)ⁿ⁻ᵏ, where C(n, k) = n! / (k!(n - k)!) is the binomial combination coefficient evaluated using log-gamma functions for large n.
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