All of the choices for one of the categories are listed in the left vertical column.
The choices for the other category are listed along the top horizontal row. If we use our breakfast example from earlier, the two-way table would look like this: Drink
Pancakes (P) Food Waffl es (W)
Coff ee (C) Juice (J) Hot chocolate (H) Tea (T) PC
PJ WC Fruit salad (F) FC Worked example
Patrick has decided to purchase a new car. The colours the garage off er are silver, black and red. The types of car are fi ve-door or three-door. (i) How many diff erent options of car are available to Patrick? (ii) List all the possible combinations of car Patrick could purchase.
Solution (i)
WJ FJ
PH
WH FH
PT
WT FT
(ii)
We can use m × n or 3 (colours) multiplied by 2 (door types)
2. Tree diagrams
A tree diagram is a way of listing all possible outcomes when combining a number of choices within two or more categories.
A tree diagram is a way of seeing all the possible probability ‘routes’ for two (or more) events. Its name comes from the fact that, when complete, the diagram looks similar to the branches of a tree. Each branch of the tree represents a diff erent outcome. When we follow the branches of the tree, we can see all of the possible outcomes.
Worked example 1 Draw a tree diagram to illustrate all the diff erent outcomes when tossing a coin twice.