# How to Draw a Tree Diagram

## Drawing a Tree Diagram

A tree diagram shows all the possible outcomes of an event and their probabilities.

For example, we can draw the tree diagram of a single coin toss.

## How to Draw a Tree Diagram

A single coin toss can be drawn on a tree diagram.

### Question

Draw a single coin toss on a tree diagram.

# 1

List the possible outcomes of the event.

If a coin is tossed, the coin can land on Heads or Tails. # 2

Draw a branch for each outcome of the event. Label each outcome. # 3

Find the probability of each outcome and write it by the the branch. • The probability of Heads is 12. It is written by the branch.

• The probability of Tails is 12. It is written by the branch.

We have drawn the tree diagram that represents the single tossing of a coin.

## How to Draw a Tree Diagram with More Than One Event

A tree diagram can be drawn for more than one event.

A coin can be tossed twice, one time after another. This can be drawn on a tree diagram.

### Question

Draw a double coin toss on a tree diagram.

### 1st Toss

Consider the first toss of the coin.

The tree diagram for the first toss will be the same as the tree diagram for a single toss. ### 2nd Toss

Consider the second toss of the coin.

We extend the tree diagram to the right.

For each branch of the 1st toss, we can draw another 2 branches, showing the same two outcomes.

#### 1st Toss Was Heads

Another tree diagram can be drawn from the Heads branch of the 1st toss. #### 1st Toss Was Tails

Another tree diagram can be drawn from the Tails branch of the 1st toss. ## Another Real Example of How to Draw a Tree Diagram

The above example was simple because the tossing of a coin is an independent event. The probability of getting Head or Tails is always the same.

Drawing a tree diagram for a dependent event is more complicated.

The slider below another real example of how to draw a tree diagram.

Open the slider in a new tab