Binomial distribution calculator

Calculate binomial probabilities P(X=k), cumulative probabilities, expected value, and standard deviation.

nkp

Models the number of successes in n independent trials, each with probability p.

P(X=k) = C(n,k) × pᵏ × (1−p)ⁿ⁻ᵏ

Flip 10 coins, P(exactly 3 heads): n=10, k=3, p=0.5. P = C(10,3)×(0.5)³×(0.5)⁷ = 120/1024 ≈ 0.117.

Mean = np. Variance = np(1−p). Standard deviation = √(np(1−p)).