Negative Binomial Probability Calculator

Instructions: Use this Negative Binomial calculator to compute negative Binomial probabilities using the form below. Please type the population proportion of success p (a number between 0 and 1), and the number of required successes r (an integer number), and provide details about the event you want to compute the probability for (notice that the numbers that define the events need to be integer):

Population proportion (p) =
Required # of successes (r) =
≤ X ≤
X ≤
X ≥

Negative Binomial Probability Calculator

More about the Negative Binomial distribution probability so you can better use this calculator: The negative binomial probability is a type of discrete probability distribution \(X\) that can take random values on the range of \([r, +\infty)\), where \(r\) is the required number of successes. In other words, \(X\) is the number of trials required to get exactly \(r\) successes. For a value \(x \in [r, +\infty)\), the negative binomial probability is computed as follows:

\[ \Pr(X = x) = \left( \begin{matrix} x-1 \\ r-1 \end{matrix}\right) p^r (1-p)^{x-r} \]

Using the above negative binomial distribution curve calculator, we are able to compute probabilities of the form \(Pr(a \le X \le b)\), of the form \(\Pr(X \le b)\) or of the form \(\Pr(X \ge a)\). Type the appropriate parameters for \(r\) and \(p\) in the text box above, select the type of tails, specify your event and compute your negative binomial probability. If instead you need to compute binomial probabilities, please check out this calculator

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