Binomial Probability Calculator — P(X = k) & Cumulative (Free)
Use this free binomial probability calculator to find the chance of exactly k successes in n independent trials. Enter n, k and the success probability p, and you’ll get P(X = k), the cumulative probabilities, and the distribution’s mean, variance and standard deviation.
How to use the calculator
- Enter the number of trials n, the number of successes k, and the success probability p.
- Press Calculate.
- Read P(X = k), the cumulative probabilities, and the summary statistics.
The binomial formula
The probability of exactly k successes is P(X = k) = C(n, k) · pᵏ · (1 − p)ⁿ⁻ᵏ, where C(n, k) counts the ways to choose which trials succeed. The mean is np and the variance is np(1 − p).
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Frequently asked questions
What is the binomial probability formula?
P(X = k) = C(n, k)·pᵏ·(1−p)ⁿ⁻ᵏ, the chance of exactly k successes in n independent trials.
What are the mean and variance?
For a binomial distribution the mean is np and the variance is np(1−p).
Original price was: $109.99.$54.99Current price is: $54.99.
Can it give cumulative probabilities?
Yes — it also reports P(X ≤ k), P(X ≥ k) and the related tails.
Original price was: $109.99.$54.99Current price is: $54.99.
Read the full lesson: learn the method step by step.
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