Binomial Experiment Calculator
Calculate exact and cumulative probabilities, mean, and variance for a binomial distribution.
How to Use
- Enter the number of trials (n) – must be a positive integer.
- Enter the probability of success (p) – a number between 0 and 1.
- Enter the number of successes (k) – must be between 0 and n.
- Click “Calculate” to see P(X = k), P(X ≤ k), mean, and variance.
Example
Scenario: Flip a fair coin 10 times (n=10, p=0.5). What is the probability of getting exactly 3 heads?
Result: P(X=3) = 0.117187, P(X≤3) = 0.171875, mean = 5, variance = 2.5.
What is a Binomial Experiment?
A binomial experiment consists of a fixed number of independent trials, each with the same probability of success. The binomial distribution models the number of successes in such an experiment. It is widely used in quality control, medical trials, survey analysis, and gambling theory.
Our calculator computes both exact probabilities (P(X = k)) and cumulative probabilities (P(X ≤ k)), along with the mean and variance, helping you quickly analyze binomial scenarios without manual calculations.