The idea, step by step
Look at the device
A fair coin gives heads and tails equal chances. On a fair spinner with equal-sized sectors, each individual sector has the same chance. If two equal sectors are labelled red and one is blue, red has more ways to occur than blue.
Do not judge only by the number of colour names. In the spinner shown, red occupies two of the four equal sectors. Blue and green occupy one each.
Explain the comparison
For same-sized counters mixed in a bag and selected without looking, each counter has the same chance. A colour with more counters has a greater chance. State the counts supporting your comparison.
More likely does not mean certain. A bag with three red and two blue counters can still produce blue. Certain means every possible result satisfies the event; impossible means none does.
| Colour | Number of counters |
|---|---|
| Red | 3 |
| Blue | 2 |
| Green | 1 |
A common trap
If red is most likely, it must be the next result.
Instead: Most likely describes a greater chance. A less likely possible result can still occur next.
See the thinking
Compare sectors
On the supplied spinner, compare red, blue and green.
- Red has two equal sectors.
- Blue and green each have one equal sector.
- Red is more likely than either one; blue and green are equally likely.
Compare counters
For the supplied bag, which colour is least likely? Is red certain?
| Colour | Number of counters |
|---|---|
| Red | 3 |
| Blue | 2 |
| Green | 1 |
- The counts are red 3, blue 2 and green 1.
- Green has the fewest counters, so it is least likely.
- Blue and green are still possible, so red is not certain.
Check your understanding
A fair spinner has six equal sectors: three A and three B. Compare A and B.
Show answer
They are equally likely.
Each letter occupies the same number of equally likely sectors.
Your turn
6 questions · 8 marks · Work at your own pace.
Read the questions online
- A fair coin is tossed once. Are heads and tails equally likely?1 mark
- A bag has 4 red and 4 blue same-sized counters. Compare red and blue.1 mark
- A bag has 5 red and 2 blue same-sized counters. Which colour is more likely?1 mark
- Which two colours have equal chances on the supplied spinner?1 mark
- A pupil says green is impossible because it is least likely in the supplied bag. Explain the mistake.2 marks
Six same-sized counters in a bag; choose without looking Colour Number of counters Red 3 Blue 2 Green 1 - Design a fair spinner with four equal sectors that gives red and blue equal chances. Describe its labels.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- A fair coin is tossed once. Are heads and tails equally likely?1 mark
Each of the two faces has the same chance.
Yes. - A bag has 4 red and 4 blue same-sized counters. Compare red and blue.1 mark
Each colour has four equally likely counters.
Equally likely. - A bag has 5 red and 2 blue same-sized counters. Which colour is more likely?1 mark
There are more red counters than blue counters.
Red. - Which two colours have equal chances on the supplied spinner?1 mark
Each has one of the four equal sectors.
Blue and green. - A pupil says green is impossible because it is least likely in the supplied bag. Explain the mistake.2 marks
Six same-sized counters in a bag; choose without looking Colour Number of counters Red 3 Blue 2 Green 1 Least likely is not the same as impossible.
Green is possible because one green counter is present. - Design a fair spinner with four equal sectors that gives red and blue equal chances. Describe its labels.2 marks
Each colour then has two equally likely sectors.
Other arrangements of those labels are also valid.
Two red sectors and two blue sectors.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum 2026
Listing outcomes; equal/unequal likelihood; repeated trials; observed frequencies.
Official curriculum source ↗