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.