Geometric Verteilung Rechner — Formel
## How to Calculate Geometric Distribution Probability
### Formula
**P(X = k) = (1-p)^(k-1) * p**
The geometric distribution models the number of trials needed to get the first success. Each trial is independent with success probability p. The probability of needing exactly k trials means k-1 failures followed by 1 success. The expected number of trials is 1/p.
### Formula
**P(X = k) = (1-p)^(k-1) * p**
The geometric distribution models the number of trials needed to get the first success. Each trial is independent with success probability p. The probability of needing exactly k trials means k-1 failures followed by 1 success. The expected number of trials is 1/p.
Lösungsbeispiel
A basketball player has a 20% free-throw rate. What is the probability the first basket is made on the 5th attempt?
- P(X=5) = (1-0.2)^(5-1) * 0.2
- = 0.8^4 * 0.2
- = 0.4096 * 0.2
- = 0.08192
- Expected trials until first success = 1/0.2 = 5