Binomial Probability Calculator
Calculate binomial probabilities, cumulative distributions, and expected values for discrete events
About this calculator
The Binomial Probability Calculator helps you determine the likelihood of achieving a specific number of successes in a fixed number of independent trials, where each trial has the same probability of success. This statistical tool is essential for analyzing discrete probability distributions in fields like quality control, medical testing, marketing research, and academic studies. It calculates exact probabilities, cumulative distributions, and expected values, making it invaluable for decision-making and risk assessment in business and scientific applications.
How to use
Enter the number of trials (n), probability of success for each trial (p), and the number of successes you want to calculate (k). The calculator will compute the exact binomial probability, cumulative probability, and display key statistics including mean and variance for your distribution.
Frequently asked questions
What is a binomial distribution?
A binomial distribution models the number of successes in a fixed number of independent trials, each with the same probability of success.
When should I use binomial probability?
Use it when you have a fixed number of independent trials with only two possible outcomes and constant success probability.
What's the difference between exact and cumulative probability?
Exact probability shows the chance of getting exactly k successes, while cumulative probability shows the chance of getting k or fewer successes.