---
title: Binomial Distribution
---

If X ~ B(n,p) then:
P(X=x) = (n/x)p^x multiplied by (1-p)^(n-x)

![Probability](https://wikimedia.org/api/rest_v1/media/math/render/svg/d33401621fb832dd2f9783e80a906d562f669008)

![Diagram](https://wikimedia.org/api/rest_v1/media/math/render/svg/38d86cba65d40f015a2b807d2b736250805abe45)

If X ~ B(n,p) then:
E(X) = np
Var(X) = np(1-p)

Binomial distributions only occur if:
- There's a fixed number of trials, n.
- Each trial should be either a success or failure.
- Probability of success (p) is constant at each trial.
- Independent trials.