Binomial Distribution Calculator

Binomial Distributions

Formulas

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

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

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.