Topics
13. Probability
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13.03 Probability as fractions

Lesson
Practice
Lesson

Are you ready?

Remember 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.

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 answer is A.

Idea summary

These are terms we have seen to describe chance:

  • Impossible: definitely will NOT happen.

  • Unlikely: there is less than a 50\% chance of it happening.

  • Even chance: there is a 50\% chance of it happening.

  • Likely: there is more than a 50\% chance of it happening.

  • Certain: definitely will happen.

Describe probability 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

The events A, B, C and D have probabilities as shown on this probability line:

The image shows 0, a half, and 1 above a number line and A B C D below. Ask your teacher for more information.
a

Which event could be 'flipping a coin and getting a tail'?

A
Event A
B
Event B
C
Event C
D
Event D
Worked Solution
Create a strategy

Remember that a coin has two outcomes: head or tail.

Apply the idea

There is an even chance of flipping a coin and getting a tail. So the probability would be between 0 and 1 at \dfrac{1}{2}.

So the correct answer is B.

b

Which event could be 'rolling a six-sided die and getting a number less than 11'?

A
Event A
B
Event B
C
Event C
D
Event D
Worked Solution
Create a strategy

Think about the possible outcomes when we roll a six-sided die.

Apply the idea

The possible outcomes of rolling a six-sided die are 1,\,2,\,3,\,4,\,5, \, 6.

Since all of the numbers on a die are less than 11, it is certain that we will get a number that is less than 11.

Certain has a probability of 1. So the correct answer is D.

Idea summary

We can use a number to represent the probability of an event. A probability of 0 means the event is impossible, a probability of \dfrac{1}{2} means the event has an even chance, and a probability of 1 means the event is certain.

Probability as a fraction

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 wirh a purple shaded section from 0 to 1 over 2 and a blue shaded section from 1 over 2 to 1.
A
A purple square with lines on it.
B
A green 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{1}{2} so it will fall to the right of \dfrac{1}{2} on the number line.

So the correct answer is B.

b

What is the chance of event X occurring?

A
Certain
B
Likely
C
Unlikely
Worked Solution
Create a strategy

Compare \dfrac{6}{10} to 0, \,\dfrac{1}{2} and 1.

Apply the idea

A probability of \dfrac{6}{10}\, is bigger than \dfrac{1}{2} so it is closerto 1 than 0. This means the event is likely to happen.

The correct answer is B.

Idea summary

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

Words for chanceNumbers for chance
\text{Impossible}0
\text{Unlikely}\text{A fraction between }0 \text{ and }\dfrac{1}{2}
\text{Even}\dfrac{1}{2}
\text{Likely}\text{A fraction between }\dfrac{1}{2} \text{ and }1
\text{Certain}1

Probabilities from a spinner

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

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Examples

Example 4

Look at this spinner:

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

Complete the table, showing the probability of each outcome.

This image shows a table of the outcomes and probabilities for the spinner. Ask your teacher for more informaion.
Worked Solution
Create a strategy

Count the number of parts for each outcome and the total number of parts, and use the formula:

\text{Probability} = \dfrac{\text{Number of parts with the outcome}}{\text{Total number of parts}}

Apply the idea

The spinner is divided into 8 equal parts. So the denominator of each probability will be 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 outcome and probability of each sector. 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 fractions 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{3+2+2+1}{8}Add the numerators
\displaystyle =\displaystyle 1
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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