Understand the idea.
Chance describes what may happen
Chance describes what could happen in a particular situation. An impossible event cannot happen; a certain event must happen. Unlikely and likely describe possibilities between these extremes, so neither word guarantees the next result.
Order chance words from impossible through unlikely and likely to certain. When two outcomes have the same chance, call them equally likely. Choose words using the setup, rather than how much you want an outcome to happen.
Use the available outcomes
For a random draw from a well-mixed bag of equal-sized balls, compare how many balls of each colour are available. Five red balls give more ways to draw red than one blue ball gives to draw blue.
Red is more likely, but blue is still possible. Green is impossible because no green ball is present. Drawing red or blue is certain because those are the only colours in this bag.
See the method in action.
A likely colour
A bag has five red balls and one blue ball. Which colour is more likely when one ball is drawn without looking?
Worked solution
- 1
Compare the available balls.
In the stated random draw, each equal-sized ball is treated as equally likely to be chosen.
- 2
Compare the colour counts.
There are more individual balls that produce a red result than a blue result.
- 3
Choose red as the more likely colour.
A greater chance does not remove the possibility of drawing the one blue ball.
Red.
Certain and impossible
A bag holds only yellow counters. Compare drawing yellow with drawing purple.
Worked solution
- 1
Check which colours are available.
The bag contains yellow counters only.
- 2
Classify drawing yellow as certain.
Every counter that can be selected is yellow.
- 3
Classify drawing purple as impossible.
No purple counter is available to select.
Yellow is certain; purple is impossible.
Try it yourself.
Check your understanding
A bag contains only red and blue balls. Is drawing green possible?
Show answer & reasoning
No; it is impossible.
Only red and blue balls are available. Since there is no green ball to select, drawing green is impossible.
Keep practising
6 worksheet questions · 8 marks
Read the questions online
- A bag contains four red balls and one blue ball. Which colour is more likely?1 mark
- A bag contains only green balls. Describe the chance of drawing a green ball.1 mark
- A bag contains only green balls. Describe the chance of drawing a red ball.1 mark
- A fair coin has a head and a tail. Compare the chances of the two outcomes.1 mark
- Order these from least to most likely: certain, impossible, likely, unlikely.2 marks
- A blue ball is unlikely to be drawn. Can it still be drawn on the next try? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A bag contains four red balls and one blue ball. Which colour is more likely?1 mark
More of the equal-sized balls are red.
Red. - A bag contains only green balls. Describe the chance of drawing a green ball.1 mark
Every possible ball is green.
Certain. - A bag contains only green balls. Describe the chance of drawing a red ball.1 mark
There are no red balls.
Impossible. - A fair coin has a head and a tail. Compare the chances of the two outcomes.1 mark
A fair coin gives the two sides equal chances.
Equally likely. - Order these from least to most likely: certain, impossible, likely, unlikely.2 marks
Impossible and certain are the two extremes.
Impossible, unlikely, likely, certain. - A blue ball is unlikely to be drawn. Can it still be drawn on the next try? Explain.2 marks
It is not the same as impossible.
Yes. Unlikely still means possible.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Ordering likelihood; independent/dependent events; repeated trials; comparing variation.
Official curriculum source ↗