Combined events
Combined events can be shown in different ways such as by systematic listing, or by using tables, grids, Venn diagramNamed after John Venn who created the term, it’s a way of identifying mathematical relationships between different groups or sets of things. and tree diagrams. The probabilityThe extent to which something is likely to be the case. of a particular combined event can then be found.
At Higher GCSE, you might also use the product rule.
Systematic listing
The outcomes for an event can be listed in an organised or systematic way to make sure that none of the possible outcomes is missed out. Look for patterns to help find all the outcomes.
Example
How many different three-digit numbers can be made using the digits 3, 6, and 9?
First, find all the numbers that can start with 3:
- 369 and 396
There will also be two numbers that start with 6 and 9:
- 639 and 693
- 936 and 963
So there are six possible numbers:
- 369
- 396
- 639
- 693
- 936
- 963