Binomial Distribution Calculator

Binomial Distributions

Formulas

A binomial experiment with n trials, probability of success p, and x successes, has
Binomial Probability: $$P(X = x) = _nC_x * p^x * (1 - p)^{n - x}$$
Where "n choose x" is: $$(_nC_x) = \frac{n!}{x! (n - x)!}$$

Mean: $$ \mu = n * p$$
Variance: $$ \sigma = n * p * (1-p)$$
Standard Deviation: $$ \sigma^2 = \sqrt{n * p * (1-p)}$$

Requirements

Binomial Experiments must have:

• Trials with 2 outcomes (success or failure)
• Independent trials (the probability of a particular outcome is constant)

p must be between 0 and 1, n and x must be positive integers where n ≥ x

Learn more on Wikipedia and Math is Fun, or watch a 3Blue1Brown video.