Overview
What Is Binomial Probability?
Binomial probability calculates the likelihood of exactly a specific number of successes across a fixed number of independent trials, each with the same success probability.
Calculate binomial distribution probability instantly.
Binomial probability calculates the likelihood of exactly a specific number of successes across a fixed number of independent trials, each with the same success probability.
Useful for coursework involving repeated independent trials, like coin flips or quality control sampling.
Input how many independent trials you're conducting.
Input the probability of success on each trial.
Input the specific number of successes you want the probability for.
The result updates automatically.
P(X=k) = C(n,k) × p^k × (1-p)^(n-k), where n is trials, p is success probability, and k is number of successes.
Trials must be independent, each trial has the same success probability, and there are only two possible outcomes (success/failure).
No, this calculates the probability of exactly k successes - 'at least' would require summing multiple probabilities.
Calculating the probability of getting exactly 3 heads in 10 coin flips.
No, calculations happen entirely in your browser.
Yes, any probability between 0 and 1 (0% to 100%).
Quality control (defect rate sampling), clinical trials, and various fields involving repeated independent trials.
No, binomial probability accounts for all possible orderings that produce the specified number of successes.
No, successes must be between 0 and the total number of trials.
Yes, completely free with no sign-up required.