Probability and Statistics > Binomial Distribution

## Binomial Distributions in Real Life

Binomial distributions are the results from experiments with two outcomes. The term “experiment” can mean a trial, a decision, or just a roll of the die. They are really just a measure of success (or failure). In other words, something happens, or it doesn’t. Will I live to 100, or won’t I? Will my car start, or won’t it? Can I pay my college tuition or not?

A simple example is buying a scratch-off lottery ticket.

You’re either going to win, or you’re not. Knowing what your odds of winning are help you to decide if you’re going to buy a ticket.

Other examples:

- You find a parking space, or you don’t.
- You win Powerball, or you don’t.
- You get a birthday gift from your partner, or you don’t.
- A drug cures, or it doesn’t.
- A computer works, or it doesn’t.
- You get a paycheck, or you don’t.

You’d want to know if a computer is going to work before you buy it. Which means that you’ve probably used binomials without realizing it. Before you buy, you might have checked reviews. While a lot of review sites have ratings, they’re mostly in two categories: it’s great, or it sucks. Whether something works or not becomes more important in life or death situations; For example, taking a drug to see if it cures terminal disease. In fact, “life” and “death” are two outcomes, which makes *anything* that could result in death a binomial.

## The Binomial Distribution: Definition

Of course, you need a little math to describe it. A binomial distribution is the probability of something happening in an experiment. There are two variables, n and p.

- n: The number of times the experiment happens.
- p: The probability of one specific outcome.

For example, if you roll a die 20 times, then “n” is 20. If you buy ten lottery tickets, then n is 10. The odds of rolling a number (like 4) are 1 out of 6. So p=(1/6). And the odds of you winning a lottery are usually high, maybe one out of a million. In that case, p would equal (1/1 million).

## Binomial Distribution: Example

If you were to roll a die 20 times, the probability of you rolling a six is 1/6. This ends in a binomial distribution of (n=20, p=1/6). For rolling an even number, it’s (n=20, p=1/2).

There are hundreds of ways you could measure success, but this is one of the simplest. Something works, or it doesn’t. It isn’t enough to say “maybe it will work”, especially if there’s money involved. For example, drugs cost billions to develop. Some medication cost patients over $50,000 a year. Before the drug is made, the manufacturer wants to know if it will work. Before you a buy a drug, you’ll want to know if it’s going to work. They can all be measured with binomials.

Imagine a life *without* binomials. You wouldn’t know what the chances are of a drug curing you. You wouldn’t know what the odds were that you would get a side effect. You wouldn’t be able to compare different drugs. And you probably wouldn’t even be able to buy it in the first place. Why? Because buying something is a binomial experiment too. Can I afford it or can’t it? Do I have money in my wallet or don’t I? Do I have enough gas in my car? And so on…!

## Articles

You’ll find lots of binomial distribution help on this site. Here are the most popular articles.

## Basic Information

- What is Bernoulli Sampling?
- What is a Binomial Distribution?
- What is a Bernoulli Distribution?
- Variance of Binomial Distribution.
- Standard deviation for a binomial distribution.
- Mean of Binomial Distribution.
- The Success/Failure Condition.

## Experiments

- Binomial Experiment: Is it one or not?
- What is a Bernoulli Trial?
- Using the Normal Approximation to solve a Binomial Problem.
- How to Work a Binomial Distribution Formula
- The Binomial Hypothesis Test.
- Another example of how to solve a problem using Binomial Formula.
- How to find the mean of the probability distribution (binomial).

## Online calculator

Binomial Distribution Calculator

## Table

Binomial Distribution Table

How to Read a Binomial Distribution Table

Check out my new YouTube channel! I’ve got 100 videos up on all kinds of stats topics. More videos coming out every week; If you’re taking a class, subscribe. Comments and suggestions are always welcome.

Have a question not covered here? Use the Google Search at the top of the page to find what you’re looking for. Or post a comment and I’ll do my best to help!