# Binomial distribution

There’s a lot of situations in life where we can be faced with two possible outcomes. For example, you either win the lottery or you don’t and a drug to cure a disease works or it doesn’t. Binomial distributions come into play. When analyzing the probability of success or failure such as these. This type of distribution evaluates the likelihood for an experiment or survey outcome to either succeed or fail – such as coins landing on heads-or-tails during tosses or passing/failing tests.

## Binomial distribution formula

Your experiment must meet the following three criteria in order to use the formula below:

1. Fixed number of observations or trials. In other words, you can have 10 trials or 100, but not an unlimited number of attempts.
2. Independent observations or trials. In other words, one coin toss or test attempt (or whatever it is you are measuring) should not affect the next attempt.
3. Same probability of success from one “trial” to another. for example, the odds of flipping heads remains at 50% from trial to trial.

The binomial distribution formula is:

b(x; n, P) = nCx * Px * (1 – P)n – x

Where:

• b = binomial probability.
x = total number of “successes.”
P = probability of a success on a single attempt.
n = number of attempts or trials.

The binomial distribution formula can also be written as: