Binomial Distribution Calculator
Calculate the probability of exactly k successes in n independent Bernoulli trials with success probability p.
How to Use the Binomial Distribution Calculator
- Enter the number of trials n, successes k, and probability p.
- Click Calculate to find P(X = k).
- The mean and standard deviation of the distribution are also shown.
Schnellreferenz
| Von | Nach |
|---|---|
| n=10, k=5, p=0.5 | P ≈ 0.2461 |
| n=20, k=0, p=0.1 | P ≈ 0.1216 |
| n=6, k=6, p=0.5 | P ≈ 0.0156 |
| n=100, k=50, p=0.5 | P ≈ 0.0796 |
| Mean = np | Expected successes |
Anwendungsfälle
- •Computing coin flip probabilities (e.g., 7 heads in 10 flips).
- •Quality control: probability of k defects in n items.
- •Survey analysis: probability of k positive responses.
Formel
P(X=k) = C(n,k) × p^k × (1−p)^(n−k). Mean = np. Std dev = √(np(1−p)).
Häufig gestellte Fragen
What is the binomial distribution?
The probability distribution for the number of successes in a fixed number of independent trials, each with the same success probability.
What is C(n,k)?
The binomial coefficient 'n choose k' = n! / (k!(n−k)!), the number of ways to choose k items from n.
When is it used?
For coin flips, defect counts, survey yes/no responses, and any fixed-trial success/failure experiment.