Negative Binomial Calculator
Calculate the probability of k trials needed to achieve r successes
About Negative Binomial Distribution
The negative binomial distribution models the number of trials needed to achieve a specified number (r) of successes.
Key Formulas:
- P(X = k) = C(k-1, r-1) × p^r × (1-p)^(k-r)
- Mean = r/p
- Variance = r(1-p)/p²
Example: How many times must you roll a die to get 3 sixes?
Note: When r = 1, this reduces to the geometric distribution.