The idea, step by step
Equal chances do not force equal counts
A fair coin has equal chances of heads and tails, but ten tosses need not give five of each. Different groups can follow the same fair procedure and record different counts. Variation means the observed results change from one batch to another.
| Group | Heads | Tails |
|---|---|---|
| A | 4 | 6 |
| B | 7 | 3 |
| C | 5 | 5 |
Compare fairly and explain cautiously
Compare batches with the same number of trials first. Check both counts and totals. A batch of seven heads from ten tosses does not prove the coin is biased. More repeated observations can help investigate a pattern, but no earlier tally guarantees the next outcome. Explain what was observed and what remains uncertain.
A common trap
Equal chances mean every small batch must split equally.
Instead: Equal chances describe the setup. Small-batch counts vary.
See the thinking
Compare equal batches
Using the supplied table, which group recorded the most heads?
| Group | Heads | Tails |
|---|---|---|
| A | 4 | 6 |
| B | 7 | 3 |
| C | 5 | 5 |
- A recorded 4, B recorded 7 and C recorded 5.
- 7 is the largest count.
A claim about the future
Group C recorded five heads and five tails. Does that guarantee its next ten tosses will also split five and five?
- A past batch describes what happened, not what must happen next.
- Independent tosses can produce a different count.
Check your understanding
Can two groups using the same fair coin rule get different results?
Show answer
Yes.
Chance variation can produce different frequencies even with the same setup.
Your turn
6 questions · 9 marks · Work at your own pace.
Read the questions online
- Using the supplied table, how many more heads did B record than A?1 mark
Practice data: three groups each toss a fair coin ten times Group Heads Tails A 4 6 B 7 3 C 5 5 - Check the total trials for Group C in the table.1 mark
Practice data: three groups each toss a fair coin ten times Group Heads Tails A 4 6 B 7 3 C 5 5 - Group D records nine heads in ten tosses. Is ten heads impossible in another batch?1 mark
- A bag trial gives red 8 times in 20 draws; another gives red 12 times in 20 draws. Describe the difference.2 marks
- Why is comparing “6 heads from 10 tosses” with “8 heads from 20 tosses” using the head counts alone unfair?2 marks
- A student says a fair coin is broken because ten tosses gave 6 heads and 4 tails. Is this enough evidence? Explain.2 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- Using the supplied table, how many more heads did B record than A?1 mark
Practice data: three groups each toss a fair coin ten times Group Heads Tails A 4 6 B 7 3 C 5 5 7 − 4 = 3.
3. - Check the total trials for Group C in the table.1 mark
Practice data: three groups each toss a fair coin ten times Group Heads Tails A 4 6 B 7 3 C 5 5 5 heads + 5 tails = 10.
10. - Group D records nine heads in ten tosses. Is ten heads impossible in another batch?1 mark
Every toss can land heads even though that batch is unusual.
No. Ten heads is possible. - A bag trial gives red 8 times in 20 draws; another gives red 12 times in 20 draws. Describe the difference.2 marks
12 − 8 = 4; the counts vary between batches.
The second batch has 4 more red outcomes. - Why is comparing “6 heads from 10 tosses” with “8 heads from 20 tosses” using the head counts alone unfair?2 marks
More trials give more opportunities for heads; compare like-sized batches or state both totals.
The groups used different trial totals. - A student says a fair coin is broken because ten tosses gave 6 heads and 4 tails. Is this enough evidence? Explain.2 marks
Repeat the experiment and examine the method rather than expecting every short batch to be equal.
No. That result can occur by chance with a fair coin.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Ordering likelihood; independent/dependent events; repeated trials; comparing variation.
Official curriculum source ↗