Negative Binomial Probability Calculator

Calculate the probability of achieving a specific number of successes in a given number of trials using the Negative Binomial Distribution.

Input Parameters

Enter the probability of success on a single trial, the desired number of successes, and the trial number to calculate the negative binomial probability.

Probability of Success (p): (0 to 1)

Number of Successes (r):

Trial Number (n):

Result

Negative Binomial Probability:

Probability Distribution Table

This table shows the probability of achieving exactly successes for different trial numbers, starting from the minimum required trials.

Trial Number (n)	Probability

Understanding Negative Binomial Probability

The Negative Binomial Distribution models the probability of achieving a specific number of successes after a certain number of trials in a sequence of independent Bernoulli trials. Unlike the binomial distribution, the number of trials is not fixed in advance. Instead, we are interested in the probability of observing the r-th success on the n-th trial.

This calculator helps you determine the likelihood of this event, given the probability of success on a single trial (p), the desired number of successes (r), and the trial number (n) at which you want to observe the r-th success. It's widely used in scenarios where you're interested in the number of trials needed to achieve a certain number of successes, such as in quality control, marketing, and research studies.

Learn more about Negative Binomial Distribution on Wikipedia.