13B.3 - Tree Diagrams

Learning intentions:

In this section we will examine:

    • How to determine probabilities of combined multi-stage random experiments.
  • The use of tree diagrams in representing sample spaces.

Tree diagrams

Tree diagrams can be used to show the outcomes in a sample space containing two or more events. If you only need to represent two event you may also consider a table or grid. Each stage in the multi-stage experiment is represented by another set of forks in the tree.

Mathematical operations with tree diagrams

When using a tree diagram remember:

    • Multiply probabilities along the branches.
    • Add probabilities down the tree.

Helpful hints:

    • Keep probabilities as unsimplified fractions so that you can check they all add up to 1. When you answer the question you should then simplify your answer!
    • If the probabilities of the branches in the same "stage" are identical up and down the tree then you are dealing with independent events. If the the probabilities are different within the same stage the events are dependent.

13B.3 - Exercises:

    1. ...

Success criteria:

You will be successful if you can:

    1. Use tree diagrams to represent complex multi-stage random experiments.
    2. Use the visual representations to calculate the probability of events.

Return to: Section 13B - Representing Sample Space