🪙 Negative Binomial Distribution

Flip coins until you get r heads - how many tails will you see?

📚 What is the Negative Binomial Distribution?

The Negative Binomial Distribution models the number of failures (tails) before achieving a fixed number of successes (heads) in a sequence of independent Bernoulli trials.

P(X = k) = C(k + r - 1, k) × p^r × (1-p)^k

Where: X = number of tails, r = target heads, p = probability of heads, k = number of tails

0.50
3

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Total Trials
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Average Tails
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Theoretical Mean
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Theoretical Variance

Distribution of Number of Tails (from all trials)

Empirical Distribution
Theoretical Distribution