Probability from Venn Diagrams (WJEC GCSE Maths & Numeracy (Double Award)): Revision Note

Probability from Venn Diagrams

What do the different regions mean on a Venn diagram?

• This will depend on how many events there are and how the outcomes overlap

• Venn diagrams show ‘AND’ and ‘OR’ statements easily

• Venn diagrams also instantly show mutually exclusive events

  • Independence can be deduced from the probabilities involved

How do I find probabilities from Venn diagrams?

• Draw, or add to a given Venn diagram, filling in as many values as possible from the information provided in the question

• It is usually helpful to work from the centre outwards

  • i.e. fill in intersections (overlaps) first

  • This is particularly crucial with Venn diagrams with three events

    • the intersection of events A and B  may include the intersection of events A, B  and C

    • a question would make it clear if a given frequency or probability is only for events A and B , and not C

• Any frequencies or probabilities not given may be able to be calculated from those that are

  • Use the results from Basic Probability to deduce missing frequencies or probabilities and answer questions

    • 

    • For independent events, 

    • For mutually exclusive events, 

How do I test for independence in a Venn diagram?

• To test if two events A and B are independent events

  • use the Venn diagram to find

    • (from the intersection of A and B)

    • (from adding up all probabilities inside the A circle)

    • (from adding up all probabilities inside the B circle)

  • then check if they satisfy

    • If they do, A and B are independent