Binomial Distribution Simulator
Simulate probability bars for repeated success/failure trials
Binomial Formulas
| Probability | P(X = k) = C(n,k)p^k(1-p)^(n-k) |
| Mean | E(X) = np |
| Variance | Var(X) = np(1-p) |
| Standard deviation | sqrt(np(1-p)) |
Step-by-Step Example
For n = 10, p = 0.5, and k = 5, use P(X = 5) = C(10,5)(0.5)^5(0.5)^5. Since C(10,5) = 252, the probability is 252 / 1024, or about 24.61%.
When to Use It
- The number of trials is fixed.
- Each trial has only success or failure outcomes.
- The success probability stays the same for every trial.
- The trials are independent.
Frequently Asked Questions
What is a binomial distribution?▼
A binomial distribution models the number of successes in a fixed number of independent trials, where each trial has the same probability of success.
What is the binomial probability formula?▼
The formula is P(X = k) = C(n,k) p^k (1-p)^(n-k), where n is trials, k is successes, and p is success probability.
What is the expected value?▼
The expected value of a binomial distribution is n times p.
What is the variance?▼
The variance is n times p times (1-p).
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