Binomial Probability Calculator
Calculate binomial probabilities for n trials with p probability of success. Find exact and cumulative probabilities with mean, variance, and standard deviation.
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Total number of independent trials
Probability for each trial (0 to 1)
Desired number of successful trials
How to Use Binomial Probability Calculator
- 1
Enter the number of trials (n).
- 2
Enter the probability of success (p) for each trial.
- 3
Enter the number of successes (k) you want to calculate.
- 4
View P(X = k), P(X ≤ k), and distribution statistics.
Frequently Asked Questions
What is binomial probability?▾
Binomial probability calculates the likelihood of getting exactly k successes in n independent trials, where each trial has the same probability p of success.
When to use binomial distribution?▾
Use when you have a fixed number of independent trials, two possible outcomes (success/failure), and constant probability across trials. Examples: coin flips, quality control sampling, medical test results.
What is cumulative probability?▾
Cumulative probability P(X ≤ k) is the sum of probabilities for 0, 1, 2, ..., k successes. It answers "what is the probability of k or fewer successes?"
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