# Tree Diagrams in Math: Definition & Examples

Coming up next: Truth Table: Definition, Rules & Examples

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

Replay
Your next lesson will play in 10 seconds
• 0:03 Tree Diagrams
• 1:53 Examples
• 4:12 Lesson Summary

Want to watch this again later?

Timeline
Autoplay
Autoplay
Speed

#### Recommended Lessons and Courses for You

Lesson Transcript
Instructor: Laura Pennington

Laura has taught collegiate mathematics and holds a master's degree in pure mathematics.

Explore what a tree diagram is and how to use it to organize information and answer questions about various outcomes of a particular event in this lesson. See how to create a tree diagram through multiple examples and a detailed explanation.

## Tree Diagrams

Have you ever been staring into your closet trying to figure out what to wear and wondered how many outfits you could actually put together with your different tops, bottoms, and shoes? In mathematics, we have a tool for this called a tree diagram. A tree diagram is a tool that we use in general mathematics, probability, and statistics that allows us to calculate the number of possible outcomes of an event, as well as list those possible outcomes in an organized manner.

A common example used to introduce tree diagrams is to find the number of possible outcomes of flipping two coins in succession. We know that when we flip a coin, it will either land on heads or tails, so when we flip one of the coins, we have two possible outcomes: heads or tails. When creating a tree diagram, we would represent this by having a starting point, then we would draw two branches from that starting point: one for heads and one for tails.

Now, when we flip the second coin, it can land on either heads or tails. Thus, we could get a heads on the first coin, and then we could get either heads or tails on the second coin, or we could get tails on the first coin, and then get either heads or tails on the second coin. In the tree diagram, we represent this by drawing two branches off of each of our last branches. These branches represent heads or tails on the flip of the second coin.

Our tree diagram displays all the possible outcomes of flipping two coins in succession. Each path of branches represents one outcome. From the diagram, we see that we have four possible outcomes:

• Tails, Tails

The coin toss example is a simple example of a tree diagram. Let's look at a few more examples to become more comfortable with this mathematical tool.

## Examples

In our first example, let's assume you are trying to put together an outfit to wear to an upcoming event you are planning to attend. You have three pairs of pants to choose from (P1, P2, P3); two tops (T1, T2); and two pairs of shoes (S1, S2). How many possible outfits can you make with these clothing items?

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.