Negative Binomial Probability Calculator

Understand the likelihood of failures before successes in repeated trials.

Calculate Negative Binomial Probability

Number of Successes (r)

Probability of Success (p)

Number of Failures (k)

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.