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11. Chance
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Stage 3

11.05 Chance of an event

Lesson
Practice
Lesson

Are you ready?

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".

A 12-sided die. Ask your teacher for more information.

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.

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Examples

Example 2

A six-sided dice is rolled.

A six-sided die.
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.

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Examples

Example 3

Look at this spinner:

A spinner with 8 sectors. 1 sector has a pig, 3 have stars, 2 have balls, and 2 have an apples.
a

Complete the table, showing the probability of each outcome.

This image shows a table of outcomes and probabilities. Ask your teacher for more informaion.
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:

This image shows a table of outcomes and probabilities. Ask your teacher for more informaion.
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
\displaystyle \text{Total probability}\displaystyle =\displaystyle \dfrac{3}{8} + \dfrac{2}{8} + \dfrac{2}{8} + \dfrac{1}{8}Add all the probabilities
\displaystyle =\displaystyle \dfrac{8}{8}Add the numerators
\displaystyle =\displaystyle 1Simplify
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

MA3-19SP

conducts chance experiments and assigns probabilities as values between 0 and 1 to describe their outcomes

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