Negative Binomial Calculator — सूत्र
## How to Calculate Negative Binomial Probability
### Formula
**P(X = k) = C(k-1, r-1) * p^r * (1-p)^(k-r)**
The negative binomial distribution models the number of trials needed to achieve exactly r successes. The last trial must be a success (the r-th), and the preceding k-1 trials must contain exactly r-1 successes. The expected number of trials is r/p.
### Formula
**P(X = k) = C(k-1, r-1) * p^r * (1-p)^(k-r)**
The negative binomial distribution models the number of trials needed to achieve exactly r successes. The last trial must be a success (the r-th), and the preceding k-1 trials must contain exactly r-1 successes. The expected number of trials is r/p.
हल किया गया उदाहरण
A salesperson closes 40% of pitches. What is the probability that the 3rd sale happens on the 8th pitch?
- Need r=3 successes on trial k=8
- C(7,2) = 21
- p^r = 0.4^3 = 0.064
- (1-p)^(k-r) = 0.6^5 = 0.07776
- P(X=8) = 21 * 0.064 * 0.07776 ≈ 0.10450
- Expected trials = 3 / 0.4 = 7.5