#### 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**