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Binomial Probability Distribution Formulas and Calculator

Engineering Math

Binomial Distribution Probability Formulas and Calculator.

There are many cases where the results of an experiment (or trial) are either it works or it doesn't, pass/fail, success/failure. Only two possible outcomes one of which we define as success the other outcome as failure. The binomial distribution is suitable if the random variable (the set of experimental or trial outcomes) when:

  • the number of trials is fixed, and
  • the probability of success is equal for all trials.


When we are interested in knowing the probability of exactly x successes in n trials that has a probability of success, p, on each trial, then the Binomial Distribution Formula may be useful.
The formula for the binomial probability mass function is


Binomial Distribution Formulas