# Probability Distribution: Definition, Formula & Example

Coming up next: Statistical Analysis with Categorical Data

### You're on a roll. Keep up the good work!

Replay
Your next lesson will play in 10 seconds
• 0:00 Probability
• 0:41 Probability Distribution
• 1:59 Non-Uniform…
• 2:41 Cumulative Distribution
• 3:58 Lesson Summary

Want to watch this again later?

Timeline
Autoplay
Autoplay
Speed

#### Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Lance Cain
Probability distribution is a way of mapping out the likelihood of all the possible results of a statistical event. In this lesson, we'll look at how that is done and how to make practical applications of this concept.

## Probability

Probability is the likelihood that an event will occur and is calculated by dividing the number of favorable outcomes by the total number of possible outcomes. The simplest example is a coin flip. When you flip a coin there are only two possible outcomes, the result is either heads or tails. And so, the probability of getting heads is 1 out of 2, or ½, or 50%. The table below shows the distribution of the probability of each outcome. There is a 50% chance the outcome will be heads, and there is a 50% chance the outcome will be tails.

## Probability Distribution

Probability distribution maps out the likelihood of multiple outcomes in a table or equation. If we go back to the coin flip example, we already know that one flip of the coin has only two possible outcomes. But if we flip the coin twice in a row, there are four possible outcomes (heads-heads, heads-tails, tails-heads and tails-tails). So now that we have a series of potential outcomes, consider the probabilities of getting heads once, twice or zero times.

The table below shows the distribution of probabilities for each possible result of getting heads in two flips of the coin, thus the table is called a probability distribution. Notice that the two middle rows both reflect the probability of getting just one heads in both flips, so these two probabilities can be combined and rewritten as a probability of 2 out of 4, or ½, or 50%.

Another plain example is that of rolling a die. A fair die has six-sides, with each side numbered from 1 to 6. Additionally, each side is equally likely to turn up when rolled. A probability distribution can be compiled like the table below, which shows the probability of getting any particular number on one roll:

To unlock this lesson you must be a Study.com Member.

### Register to view this lesson

Are you a student or a teacher?

#### See for yourself why 30 million people use Study.com

##### Become a Study.com member and start learning now.
Back
What teachers are saying about Study.com

### Earning College Credit

Did you know… We have over 200 college courses that prepare you to earn credit by exam that is accepted by over 1,500 colleges and universities. You can test out of the first two years of college and save thousands off your degree. Anyone can earn credit-by-exam regardless of age or education level.