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.

Step-by-Step:

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.

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.

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

See Also

What is probability? What are dependent events? What are independent events?