Binomial Distribution Calculator
Calculate binomial probabilities for a fixed number of independent trials. Find the probability of exactly k successes, at most k successes, or at least k successes.
The binomial distribution models the number of successes in n independent trials, each with probability p.
PMF (Probability Mass Function): P(X = k) = C(n,k) × p^k × (1-p)^(n-k)
Where C(n,k) = n! / (k!(n-k)!) is the binomial coefficient.
Key Properties
- Mean: E(X) = n × p
- Variance: Var(X) = n × p × (1-p)
- Standard deviation: σ = √(n × p × (1-p))
Examples
- Coin flips (p = 0.5)
- Quality control defects
- Survey yes/no responses