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.
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.