 # 11.05 Chance of an event

Lesson

## Ideas

Can you list all the  outcomes  from an experiment? Can you count how many match a description?

### Examples

#### Example 1

Sally rolls a twelve-sided die and writes down whether she rolls 6 or more. If she does, she writes "yes", otherwise she writes "no".

Which of the following is the list of outcomes where she writes "yes"?

A
2,\ 4, \ 6, \ 8, \ 10, \ 12
B
1, \ 2, \ 3, \ 4, \ 5, \ 6
C
6, \ 7, \ 8, \ 9, \ 10, \ 11, \ 12
Worked Solution
Create a strategy

List the outcome of rolling a 6 or more.

Apply the idea

The die has 12 sides. The outcomes for rolling a 6 or more are: 6, \, 7, \, 8, \, 9, \, 10, \, 11, \, 12.

So the correct answer is option C.

Idea summary

The outcomes for an experiment are the possible results that could happen.

## Probability as fractions

This video looks at how to find the probability for an event as a fraction.

### Examples

#### Example 2

A six-sided dice is rolled.

a

What is the probability of rolling a four?

Worked Solution
Create a strategy

Use the formula: \text{Probability} = \dfrac{\text{Number of faces showing a four}}{\text{Total number of faces}}

Apply the idea

There are 6 faces on a die and 4 appears on a die 1 time.

This means that the probability of rolling a 4 on a standard die is:\text{Probability} = \dfrac{1}{6}

b

What is the probability of rolling an odd number?

Worked Solution
Create a strategy

Use the formula: \text{Probability} = \dfrac{\text{Number of faces showing an odd number}}{\text{Total number of faces}}

Apply the idea

There are 6 faces on a die and the odd numbers 1, \, 3, \, 5 appear on 3 of the faces.

This means that the probability of rolling an odd number on a standard die is:\text{Probability} = \dfrac{3}{6}

Idea summary

We can write the probability of an event as a fraction using the formula \text{Probability} = \dfrac{\text{Number of what we want to happen}}{\text{Total number of outcomes}}

## Probabilities in total

This video looks at finding the probability of an event from a spinner.

### Examples

#### Example 3

Look at this spinner:

a

Complete the table, showing the probability of each outcome.

Worked Solution
Create a strategy

Use the formula:

\text{Probability} = \dfrac{\text{Number of parts we want}}{\text{Total number of parts}}

Apply the idea

The spinner is divided into 8 equal parts so the total number of parts is 8.

There are 3 stars on the spinner. So the probability of a star is \dfrac{3}{8}.

There is 1 pig on the spinner. So the probability of a pig is \dfrac{1}{8}.

Filling in the table, we get:

b

What is the sum of the probabilities for each outcome?

Worked Solution
Create a strategy

Add all the data in the Probability column.

Apply the idea
Idea summary

The probability of something happening can be written as a fraction. If there are 3 of what we want, out of a total of 10, then we have 3 chances out of 10 of it happening. As a fraction, it's \dfrac{3}{10}.

### Outcomes

#### VCMSP203

List outcomes of chance experiments involving equally likely outcomes and represent probabilities of those outcomes using fractions