The idea, step by step
A number for a chance
Probability describes how likely an event is. Zero means impossible in the model and one means certain. A probability between zero and one describes an uncertain event. For example, one half is halfway between impossible and certain.
For equally likely individual outcomes, count the outcomes that match the event and divide by the number of all possible outcomes. Use the same kind of outcome for both counts: if you count tokens in the numerator, count tokens in the denominator too.
Check the model first
A fair six-sided die has six equally likely face outcomes. A bag of matching tokens can be modelled by assuming it is mixed well and each token has the same chance of being selected. Colour names are not necessarily equally likely if there are different numbers of tokens.
This spinner has four equal-sized numbered sectors, so each number has probability one quarter. Two sectors are even, so the probability of an even number is two quarters. If sectors were unequal, simply counting their labels would not be enough.
A common trap
There are two colours, so each colour must have probability one half.
Instead: Count matching tokens, not colour names. Different numbers of equally likely tokens give different colour probabilities.
See the thinking
A mixed bag
A well-mixed bag holds 3 blue and 2 red matching tokens. Find the probability of selecting blue.
- There are tokens in total.
- Three of them are blue.
- Each token is equally likely, so divide favourable by total.
An event with two outcomes
Find the probability that a fair six-sided die shows a number greater than 4.
- The matching faces are 5 and 6: 2 outcomes.
- There are 6 possible equally likely faces.
- Write and simplify .
Check your understanding
A fair die is numbered 1 to 6. What is the probability of rolling 8?
Show answer
0.
There is no face labelled 8, so the event is impossible in this model.
Your turn
6 questions · 11 marks · Work at your own pace.
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.
. - 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.
. - 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.
. - 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.
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 ↗