Numerical likelihood | Year 6

01 / LEARN

Understand the idea.

A number for a chance

Probability places a chance on a scale from $0$ to $1$ . An impossible event has probability $0$ ; a certain event has probability $1$ . A value between them describes an uncertain event, with larger values meaning greater likelihood.

When individual outcomes are equally likely, count the outcomes that satisfy the event and divide by the total number of outcomes. Count the same kind of thing in both places: favourable tokens over all tokens, or favourable die faces over all faces.

P (event) = \frac{favourable outcomes}{all equally likely outcomes}

Check the model first

Check why the outcomes have equal chances before counting. A fair six-sided die has six equally likely faces. For matching tokens mixed well in a bag, each token has the same chance, but colours can have different chances because their token counts differ.

The supplied spinner has four equal sectors, so each numbered sector has probability $\frac{1}{4}$ . The event even number contains two sectors, giving $\frac{2}{4} = \frac{1}{2}$ . Unequal sectors would require their sizes to be considered, rather than simply counting labels.

02 / WORKED EXAMPLES

See the method in action.

EXAMPLE 01

A mixed bag

A well-mixed bag holds 3 blue and 2 red matching tokens. Find the probability of selecting blue.

Worked solution

1
Count all possible tokens.
$3 + 2 = 5$
The whole bag contains three blue tokens and two red tokens.
2
Count the favourable tokens.
$blue tokens = 3$
Selecting blue is the event being asked about.
3
Divide favourable by total.
$P (blue) = \frac{3}{5}$
The well-mixed matching tokens are equally likely, so three of the five individual outcomes give blue.

Answer

$3 / 5$ .

EXAMPLE 02

An event with two outcomes

Find the probability that a fair six-sided die shows a number greater than 4.

Worked solution

1
List the favourable faces.
$5, 6$
Greater than four excludes four itself, leaving two matching faces.
2
Count every possible face.
$1, 2, 3, 4, 5, 6$
A fair six-sided die has six equally likely face outcomes.
3
Form and simplify the probability.
$P (greater than 4) = \frac{2}{6} = \frac{1}{3}$
Two favourable faces out of six gives two sixths; dividing both parts by two gives one third.

Answer

$1 / 3$ .

03 / YOUR TURN

Try it yourself.

Check your understanding

A fair die is numbered 1 to 6. What is the probability of rolling 8?

Show answer & reasoning

The possible faces are $1$ to $6$ , so none is labelled $8$ . There are zero favourable faces out of six: $P (8) = \frac{0}{6} = 0$ .

Keep practising

6 worksheet questions · 11 marks

Open worksheet Worked solutions

Read the questions online

What probability describes a certain event?
1 mark
A bag contains 4 green and 6 yellow matching tokens. Find the probability of green.
2 marks
Find the probability of an odd result on a fair six-sided die.
2 marks
Using the equal-sector spinner, find the probability of a number less than 3.
2 marks
A bag contains only red tokens. Find the probability of not selecting red.
2 marks
A spinner has one large sector and one small sector. Can you decide that each sector has probability one half just because there are two labels? Explain.
2 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

What probability describes a certain event?
1 mark
One represents the whole set of possible outcomes.
1.
A bag contains 4 green and 6 yellow matching tokens. Find the probability of green.
2 marks
There are 10 tokens in total and 4 favourable tokens.
$\frac{4}{10} = \frac{2}{5}$ .
Find the probability of an odd result on a fair six-sided die.
2 marks
Odd faces are 1, 3 and 5: three of six faces.
$\frac{3}{6} = \frac{1}{2}$ .
Using the equal-sector spinner, find the probability of a number less than 3.
2 marks
The favourable sectors are 1 and 2.
There are four equal sectors.
$\frac{2}{4} = \frac{1}{2}$ .
A bag contains only red tokens. Find the probability of not selecting red.
2 marks
Every possible token is red; there are no favourable tokens for not red.
0.
A spinner has one large sector and one small sector. Can you decide that each sector has probability one half just because there are two labels? Explain.
2 marks
Equal label counts do not make unequal-sized sectors equally likely.
The sector sizes and spinner model must be considered.
No.

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Curriculum reference & lesson scope

Australian Curriculum v9.0; SA Mathematics Curriculum 2026

Numerical likelihood; fractions/decimals/percentages; expected versus observed outcomes; larger simulations and variation.

Official curriculum source ↗

In this lesson

Understand the idea.

A number for a chance

Check the model first

See the method in action.

A mixed bag

Count all possible tokens.

Count the favourable tokens.

Divide favourable by total.

An event with two outcomes

List the favourable faces.

Count every possible face.

Form and simplify the probability.

Try it yourself.

Check your understanding

Keep practising