Binomial Distribution Calculator

Calculate probabilities for the binomial distribution

Number of Trials (n):

Probability of Success (p):

Number of Successes (k):

P(X = 5): 24.6094%

P(X ≤ 5): 62.3047%

P(X > 5): 37.6953%

Binomial Coefficient C(10,5): 252

Mean (Expected Value): 5.0000

Variance: 2.5000

Standard Deviation: 1.5811

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

PMF: P(X = k) = C(n,k) × p^k × (1-p)^(n-k)

Mean: μ = np

Variance: σ² = np(1-p)