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Binomial Probability Calculator

Calculate the probability of exactly k successes in n independent trials.

Parameters

n (number of trials)

k (number of successes)

p (probability of success on each trial)

Probability Distribution

Binomial Distribution Properties

Mean

μ = n × p

Expected number of successes

Variance

σ² = n × p × (1-p)

Spread of the distribution

Standard Deviation

σ = √(n × p × (1-p))

Typical deviation from mean

Frequently Asked Questions

When can I use the binomial distribution?

Use binomial when you have: (1) a fixed number of trials n, (2) each trial has two outcomes (success/failure), (3) trials are independent, and (4) probability p is constant for each trial.

Examples of binomial experiments

Flipping a coin 10 times and counting heads, free throw shots, quality control (defective/not defective), multiple choice guessing, and medical treatment success rates.

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