Binomial Distribution

The binomial distribution is used for multiple Bernouli Trials.

Its formula is written as follows:

p(x) = (n choose x) p^x * (1-p)^n-x , x=0,1,2,....,n

The n choose x part is combinatorial.

n choose x = n! / x!(n-x)! where n is the number of outcomes, and x is the number of outcomes desired.

Example:
Suppose you take a true or false test with 10 questions, what are the chances you get 7 questions right if you just take random guesses? This is a true false so p=50% or .5

p(x) = (10 choose 7) (.5)⁷*(.5)³

= 10! / 7!*3! *.0078 * 0.125 = 30 * .0078 * 0.125 = 0.029

So you would only have about a 3% chance! Quite amazing. Of course, this means you would have a 97% chance of getting at least 3 wrong, which is not so amazing when you think about it.