Binomial Wahrscheinlichkeit Rechner — Formel
## How to Calculate Binomial Probability
### Formula
**P(X = k) = C(n,k) * p^k * (1-p)^(n-k)**
The binomial distribution models the number of successes in n independent trials, each with the same probability p. C(n,k) counts the number of ways to arrange k successes among n trials. The mean is np and the variance is np(1-p).
### Formula
**P(X = k) = C(n,k) * p^k * (1-p)^(n-k)**
The binomial distribution models the number of successes in n independent trials, each with the same probability p. C(n,k) counts the number of ways to arrange k successes among n trials. The mean is np and the variance is np(1-p).
Lösungsbeispiel
Flip a fair coin 10 times. What is the probability of exactly 3 heads?
- C(10,3) = 10! / (3! * 7!) = 120
- p^k = 0.5^3 = 0.125
- (1-p)^(n-k) = 0.5^7 = 0.0078125
- P(X=3) = 120 * 0.125 * 0.0078125 = 0.1171875
- Expected value = 10 * 0.5 = 5