Topics
15. Probability
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Stage 3

15.04 Probability with fractions

Lesson
Practice
Lesson

Are you ready?

Do you remember how to describe the likelihood of an event happening?

Examples

Example 1

Which section describes the chance of 'the next person you meet has the same birthday as you'?

This image shows Impossible, Even chance and Certain on a chart. Ask your teacher for more information.
A
A purple square with lines on it.
B
A green square with lines on it.
Worked Solution
Create a strategy

Think about how often you meet someone with the same birthday as you.

Apply the idea

It is unlikely that the next person you meet has the same birthday as you.

An unlikely event will have a chance between impossible and even chance, which is described by the purple section.

The correct option is A.

Idea summary

We can represent likelihood like a number line. We start with impossible events on the left and as we move right the events are more likely.

An arrow going to the right to show the order of chances from impossible, unlikely, even, likely, to certain.

Describe probabilities with numbers

We have heard about certain and impossible events, this video shows how these can be represented using a number.

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Examples

Example 2

Which of these events has a probability of 0?

A
It being cloudy tomorrow.
B
The sun not coming up tomorrow.
C
The sun coming up tomorrow.
Worked Solution
Create a strategy

Think which of the options is impossible to happen.

Apply the idea

A probability of 0 means the event is impossible.

It is impossible for the sun not to rise the next day. So the correct answer is option B.

Idea summary

If an event has a probability of 0 then the event is imposiible.

If an event has a probability of 1 then the event is certain.

Likelihood as fractions

This video shows you how likelihoods can have fractional representation.

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Examples

Example 3

Event X has a probability of \dfrac{6}{10}.

a

If event X was placed on the number line, which section would it be placed in?

A number line with a purple shaded section from 0 to a half and a blue shaded section from a half to 1.
A
A purple square with lines on it.
B
A blue square with lines on it.
Worked Solution
Create a strategy

Compare \dfrac{6}{10} to \dfrac{1}{2}.

Apply the idea

\dfrac{6}{10} is greater than \dfrac{5}{10} =\dfrac{1}{2}, so it will fall on the right side of \dfrac{1}{2} the number line which is in the blue section.

The correct answer is option B.

b

What is the chance of event X occurring?

A
Certain
B
Likely
C
Unlikely
Worked Solution
Create a strategy

Compare the value to the numbers on the probability number line.

Apply the idea

A probability of \dfrac{6}{10}\, is between \dfrac{1}{2} and 1, so the event is likely to happen. The correct answer is option B.

Idea summary

We can use numbers as well as words to describe chance:

Words for chanceNumbers for chance
\text{Impossible}0
\text{Unlikely}\dfrac{1}{4}
\text{Even}\dfrac{1}{2}
\text{Likely}\dfrac{3}{4}
\text{Certain}1

Outcomes

MA3-19SP

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

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