Statistics

Negative Binomial Distribution Calculator

Find the probability of k failures before r successes.

Calculated Output

P(X = k) 0.1875

Formula: P = C(k+r−1, k)·pʳ·(1−p)ᵏ

Step-by-Step Breakdown

1. Values used:

2. Target successes (r) = 3

3. Success probability = 0.5

4. Failures (k) = 2

6. P(X = k) = 0.1875

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The math behind it

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

r 3, p 0.5, k 2 → P ≈ 0.1875.

How is it different from binomial?

Binomial fixes the number of trials; this fixes the number of successes.