Binomial Neg PMF (simpl)
- Created by
- Renato Passos, Eng. de Software
- Reviewed by
- Renato Passos, Eng. de Software
Last updated: Apr 18, 2026
About this calculator
The Binomial Negative PMF (Probability Mass Density) is a formula used to calculate the probability of obtaining a specific number of successes in a sampling with n trials, with a probability of success p in each trial.
It is often used in sampling problems, where one wants to calculate the probability of obtaining a specific number of individuals with a characteristic in a random sample of a population.
The Binomial Negative PMF formula is given by C(k−1,r−1)pʳ(1−p)^(k−r), where C(k−1,r−1) is the binomial coefficient, p is the probability of success in a trial and r is the number of desired successes.
This formula is useful in a variety of contexts, including engineering, economics and social sciences, where one needs to calculate probabilities in sampling problems.
Frequently asked questions
What is the Binomial Negative PMF?
The Binomial Negative PMF is a formula used to calculate the probability of obtaining a specific number of successes in a sampling.
When to use the Binomial Negative PMF formula?
Use the Binomial Negative PMF formula in sampling problems, where one wants to calculate the probability of obtaining a specific number of individuals with a characteristic in a random sample of a population.
What is the binomial coefficient?
The binomial coefficient is a term that appears in the Binomial Negative PMF formula and is calculated as C(k−1,r−1)
Why is the Binomial Negative PMF formula important?
The Binomial Negative PMF formula is important because it allows calculating probabilities in sampling problems, which is fundamental in a variety of contexts.
How to calculate the probability of success p?
The probability of success p is calculated as the number of successes divided by the total number of trials.