This calculator finds Binomial probabilities associated with a provided probability of success (p) and the number of failures until the first success (x).

Enter the required values, then click the `Calculate`

button.

P(X = ):

P(X < ):

P(X ≤ ):

P(X > ):

P(X ≥ ):

## About the Geometric Distribution

The geometric distribution is a discrete probability distribution that represents the probability of a given number of successive failures before a success is obtained in a Bernoulli trial. A Bernoulli trial is an experiment with only two possible outcomes, in other words: yes/no or success/failure.

A geometric distribution is concerned only with the first success. The random variable x counts the number of trials required to obtain that first success.

The negative binomial distribution is a discrete probability distribution that models the number of failures in a sequence of Bernoulli trials before a specified number of successes (r) occurs. A geometric distribution is a special negative binomial distribution, where the number of successes r equals 1.