### Binommial Distribution Formula

P(x) = (n! / (n - x)!x!)p^{x}q

^{n-x}

n: The number of trials

x: The number of successes

p: The probability of success

q: The probability of failure (which is 1 - p)

The **binomial distribution**** ** describes the behavior of a count of variable *X* if the following conditions apply:

**1-**The number of observations n is fixed.**2-**Each observation is independent.**3-**Each observation represents one of two outcomes ("success" or "failure").**4-**The probability of "success" p is the same for each outcome.

### Sample Binomial Distribution Problem

Alex has a nickel and he is going to flip it 3 times, what is the probability of the coin flips resulting in 2 heads?Below is the possible results:

HHH, HHT, HTH, THH, TTH, THT, HTT, TTT

To solve for this problem using the formula, it will look like the following:

n: 3 (3 flips)

x: 2 (there are only two alternatives, heads or tails)

p: .5 (there is a 50% probability of getting heads)

q: .5 (there is a 50% probability of getting tails)

P(2 heads) =

(3! / (3 - 2)!2!).5

^{2}.5

^{3-2}

The answer to this problem is .375, which means there is a 37.5% probability of 2 heads occuring out of 3 flips.