Binomial Distribution Calculator
Calculate binomial probability P(X = k), P(X ≤ k), and P(X ≥ k) given number of trials, probability of success, and number of successes.
Enter n, p, and k.
Binomial Probability Formula
P(X = k) = C(n,k) × p^k × (1−p)^(n−k)
Mean = np, Variance = np(1−p)
Mean = np, Variance = np(1−p)
Example: Flip a coin 10 times (p = 0.5). P(exactly 3 heads)?
P(X=3) = C(10,3) × 0.5³ × 0.5⁷ = 120 × 0.000977 = 0.1172 (11.72%)
P(X=3) = C(10,3) × 0.5³ × 0.5⁷ = 120 × 0.000977 = 0.1172 (11.72%)
FAQ
When is the binomial distribution used?
When you have a fixed number of independent trials, each with the same probability of success (coin flips, pass/fail tests, yes/no surveys).
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Last updated: 2026-08-08