basic

Negative Binomial Failures Before k-th Success

P(X=r) = C(r+k−1,r)·(1−p)^r·p^k — failures before k successes.

Calculates the probability of exactly r failures before the k-th success in independent Bernoulli trials using the negative binomial distribution.

Priya Venkatesan By Priya Venkatesan
Published Last reviewed 1 min read

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Formula

P(X=r) = C(r+k−1, r) × p^k × (1−p)^r

In depth

Calculates the probability of exactly r failures before the k-th success in independent Bernoulli trials using the negative binomial distribution.