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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.

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. draw_tree_coin_toss_1st_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.draw_tree_coin_toss_2nd_toss_1

1st Toss Was Tails

Another tree diagram can be drawn from the Tails branch of the 1st 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.
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This page was written by Stephen Clarke.

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What Is Probability?

A probability is a measure of how likely (how probable) an event is to happen. A probability is expressed as a number between 0 (impossible) and 1 (certain). The formula for finding a probability is shown below: probability_formula_mini