Listing Outcomes

Sometimes a systematic way is needed to list all the outcomes. 

Example: Two bags each contain one red, one yellow and one green disc. 

A disc is taken from each bag. List all the possible outcomes. 

Note that we start with the red disc from the first bag and list the outcomes, then the yellow disc from the first bag and finally the green disc from the first bag. 

This provides us with nine possible outcomes. 

Using this list, we can work out the probability of an event.

Possibility Space 

For more complicated situations, we can use a table to list all the outcomes. 

Example: Throwing a coin and a dice, list all the outcomes. 

This can be done by using a possibility space, as shown below.

There are 12 possible outcomes. It can be used to calculate probabilities as follows:

Calculate the probability of getting an even number and a head.

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Tree Diagrams 

This is a way of setting down the outcomes with their probabilities for two or more events (combined). 

Example: A bag contains four green and six blue discs. A disc is selected at random and replaced, then another one is selected. What is the probability that both discs are the same colour? 

The outcomes are put on the end of branches as shown. The probabilities are put on the branches.
 

For both discs to be the same colour, we need two greens or two blues.

When moving along the branches, we multiply the probabilities as follows: 

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Example: For one thousand throws of a coin, the expected number of heads = 1/2 x 1 000 = 500.

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