13B.1 - Venn Diagrams

Learning intentions:

In this section we will examine:

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

Venn diagrams

A Venn diagram is a visual display that can be used to organise and categorise sets (events) within a sample space. All possible outcomes, the sample space, are represented with a rectangle. Within that rectangle are circles which are used to represent events of the scenario. Theoretically, there is no limit to the number of circles (events) that a Venn diagram can have; however, more than 3 or 4 circles does get exceptionally difficult. The following Venn diagram shows Venn diagrams for 2 events and 3 events:

When a circle overlaps with another circle, the overlapping region is the intersection (∩) which contains all elements that are common to all over lapping circles (events). For more information on intersections and set theory see section 1A.

YouTube Video

13B.1 - Exercises:

    1. ...

Success criteria:

You will be successful if you can:

    1. Use Venn 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