Enter n, p, and k to calculate binomial probability.

The binomial distribution is a discrete probability distribution that models the number of successes in a fixed number of independent trials, each with the same probability of success. It is widely used in statistics, quality control, medicine, and social sciences. The theoretical formula for the probability of exactly k successes in n trials is: P(X = k) = C(n,k) · p^k · (1-p)^(n-k), where C(n,k) is the binomial coefficient (number of ways to choose k successes from n trials), p is the probability of success on a single trial, and (1-p) is the probability of failure. This calculator computes the exact probability for a given k, as well as cumulative probabilities (P(X ≤ k), P(X < k), P(X ≥ k)). It also provides the mean (μ = n·p), variance (σ² = n·p·(1-p)), and standard deviation. The binomial distribution is essential for hypothesis testing, A/B testing, and predicting outcomes in scenarios with binary outcomes.

1. Enter the Number of Trials (n) – the total number of independent experiments.
2. Enter the Probability of Success (p) – the chance of success in each trial (0 to 1).
3. Enter the Number of Successes (k) – the specific number of successes you want to evaluate.
4. Click Calculate Probability to compute binomial probabilities.
5. The result shows exact probability, cumulative probabilities, mean, variance, and standard deviation.
6. Click Reset to restore default example values.