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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.
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13B.1 - Exercises:
- ...
Success criteria:
You will be successful if you can:
- Use Venn diagrams to represent complex multi-stage random experiments.
- Use the visual representations to calculate the probability of events.
Return to: Section 13B - Representing Sample Space
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