What is Negative Binomial?

It models the number of trials required to achieve a specified number of successes (r).

Difference from Geometric?

Geometric is a special case of Negative Binomial where r = 1 (trials until FIRST success). NegBin is trials until r-th success.

How many penalty kicks does a player need to take to score exactly 3 goals, if success rate is 70%?

Calculate probability of needing k trials to achieve r successes.

Probability of Success (p)

0 < p <= 1

Target Successes (r)

Total Trials (k)

Must be >= r (3)

P(X = 6)

P(X ≤ 6) = 0

Expected Trials (Mean)

Variance

Formulas

PMF

Mean

Variance

Frequently Asked Questions

How to Use

What it calculates

This negative binomial solves mathematical and statistical problems using standard formulas. Trials needed for r successes.

When to use it

Use for homework, data analysis, exam prep, or quick verification of manual calculations.

Example

Adjust the inputs above to model your specific scenario with the Negative Binomial.

Explore More

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