Drawing a Tree Diagram
(KS3, Year 7)

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.

Step-by-Step:

1

List the possible outcomes of the event. If a coin is tossed, the coin can land on Heads or Tails. heads_or_tails

2

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

draw tree coin toss step 2

3

Find the probability of each outcome and write it by the the branch. draw_tree_coin_toss_step_3

The probability of Heads is ¹⁄₂. It is written by the branch.
The probability of Tails is ¹⁄₂. It is written by the branch.

Answer:

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.

1^st 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. draw_tree_coin_toss_1st_toss

2^nd Toss

Consider the second toss of the coin. We extend the tree diagram to the right. For each branch of the 1^st toss, we can draw another 2 branches, showing the same two outcomes.

1^st Toss Was Heads

Another tree diagram can be drawn from the Heads branch of the 1^st toss. draw_tree_coin_toss_2nd_toss_1

1^st Toss Was Tails

Another tree diagram can be drawn from the Tails branch of the 1^st toss. draw_tree_coin_toss_2nd_toss_2

Lesson Slides

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.

This page was written by Stephen Clarke.

Drawing a Tree Diagram
(KS3, Year 7)