Statistics

Negative Binomial Probability Calculator

Easily calculate negative binomial probability online. Determine the probability of a specific number of failures before achieving a set number of successes in Bernoulli trials. Free, user-friendly, and accurate.

Calculate Negative Binomial Probability

Calculation Result

The probability of getting failures before successes, with a success probability of is:

Probability Visualization

Probability level:

Formula Used
$$P(X=k) = {\binom{k+r-1}{k}} \times p^r \times (1-p)^k$$

Understanding Negative Binomial Probability

The Negative Binomial Distribution calculates the probability of observing a specific number of failures before achieving a predetermined number of successes in a series of independent Bernoulli trials. Each trial has only two outcomes: success or failure, with a constant probability of success.

This tool is useful in scenarios where you\'re interested in the number of failures that occur before a certain number of successes are reached. For example, in sales, it could represent the number of no-sales before closing a certain number of deals.

Key terms:

  • r (Number of successes): The target number of successful outcomes.
  • p (Probability of success): The likelihood of success in a single trial (between 0 and 1).
  • k (Number of failures): The number of failures observed before achieving 'r' successes.

Learn more about Negative Binomial Distribution on Wikipedia and other statistical resources.

Frequently Asked Questions

What is the Negative Binomial Probability Calculator?
The Negative Binomial Probability Calculator is an online Statistics calculator. You enter your values, and it returns the answer with the steps shown so you can follow along.
How accurate is the Negative Binomial Probability Calculator?
The solver uses a math engine that avoids the floating-point rounding errors you get from most hardware calculators. For typical homework and professional calculations, the results will match what you would get by hand.
Can I use the Negative Binomial Probability Calculator for professional Statistics projects?
Yes. The math behind it is standard Statistics, so the results are reliable for professional use. That said, always double-check that your inputs are in the right format before relying on the output.
Why use the Negative Binomial Probability Calculator instead of calculating by hand?
Manual calculation is slow and error-prone, especially with multiple steps. This tool does the arithmetic for you and shows each step, so you can catch mistakes before they carry forward.
How do I format my inputs for the Negative Binomial Probability Calculator?
Type your numbers into the input fields. Leave out units and symbols unless a field specifically asks for them. The solver handles the rest.