Understand the idea.
Look at the device
To compare chances, find results that are equally likely. A fair coin gives heads and tails equal chances. On the shown fair spinner, each of the four equal sectors has the same chance, but a colour can occupy more than one sector.
Count the sectors belonging to each colour. Red covers two, while blue and green cover one each. Red therefore has twice as many equally likely sectors as either colour alone; blue and green have equal chances because their sector counts match.
Explain the comparison
For same-sized counters thoroughly mixed and selected without looking, treat individual counters as equally likely. Compare colour counts: more counters of one colour give more ways to select it. State the counts so another person can check your comparison.
Most likely still allows other outcomes. Red may have the greatest count while blue and green remain possible. A result is certain only when every possible selection gives it, and impossible only when no selection can give it.
| Colour | Number of counters |
|---|---|
| Red | 3 |
| Blue | 2 |
| Green | 1 |
See the method in action.
Compare sectors
On the supplied spinner, compare red, blue and green.
Worked solution
- 1
Count the equal sectors for each colour.
The fair spinner has four equal sectors, so each sector supplies one equally likely way for its colour to occur.
- 2
Compare red with each other colour.
Red has more equally likely sectors than blue alone or green alone, making red the most likely colour.
- 3
Compare blue with green.
One equal sector belongs to each colour, so their chances are equal.
Red is most likely; blue and green have equal chances.
Compare counters
For the supplied bag, which colour is least likely? Is red certain?
| Colour | Number of counters |
|---|---|
| Red | 3 |
| Blue | 2 |
| Green | 1 |
Worked solution
- 1
Read and compare the three counter counts.
The same-sized counters are mixed and chosen without looking, so each individual counter is treated as equally likely.
- 2
Identify green as the least likely colour.
Green has just one counter, fewer than either blue or red.
- 3
Check how many counters are not red.
Three possible selections are blue or green; because red is not the only possible result, it is not certain.
Green is least likely. Red is not certain.
Try it yourself.
Check your understanding
A fair spinner has six equal sectors: three A and three B. Compare A and B.
Show answer & reasoning
They are equally likely.
A and B each occupy three of the same six equal sectors. Their counts match, and every sector is equally likely on this fair spinner, so A and B have equal chances.
Keep practising
6 worksheet questions · 8 marks
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 ↗