The idea, step by step
Same setup, different counts
Chance results are not a repeating number pattern. Two children can each toss the same fair coin 10 times and get different counts. They can also happen to get the same counts.
Variation means these differences in results. A run of heads does not mean tails is due. The coin has no memory of earlier tosses.
Describe what happened
Check that experiments have the same number of trials before comparing their counts. Say what actually happened using the numbers. Do not turn that record into a promise about the next toss.
More trials give more information, but they do not make the next result certain. A short uneven run alone does not prove that equipment is unfair.
| Child | Heads | Tails |
|---|---|---|
| Ella | 7 | 3 |
| Noah | 4 | 6 |
A common trap
The next result must fix an uneven record.
Instead: Chance does not promise a balancing result. Record what happens, rather than forcing equal counts.
See the thinking
Compare two records
Ella has 7 heads from 10 tosses. Noah has 4 heads from 10 tosses. How many more did Ella record? Does this make Noah’s record wrong?
- 7 − 4 = 3 more heads.
- Both records total 10 tosses.
- Different counts can happen by chance.
What happens next?
A fair coin gives heads three times in a row. Must the next result be tails?
- Both faces remain on the coin.
- Previous tosses do not remove heads.
- The next result is still uncertain.
Check your understanding
Two groups each toss a fair coin 8 times. Must their head counts match?
Show answer
No.
Counts can vary even when the setup and trial totals match.
Your turn
6 questions · Work at your own pace.
Read the questions online
- Tia records 6 heads and 4 tails. Ben records 5 heads and 5 tails. They each tossed 10 times. Could both records be honest? Explain.
- A coin lands tails four times. Is tails impossible next time?
- Two die experiments each have 12 rolls. One has 4 sixes; the other has 1 six. Find the difference.
- Which statement recognises uncertainty: “I might get blue next” or “I must get blue next”?
- A record has 9 heads and 1 tail in 10 tosses. Should it be changed to 5 and 5? Explain.
- Give possible counts for two imaginary ten-toss experiments. The head counts must differ, and each pair must total 10.
Read the worked solutions
- Tia records 6 heads and 4 tails. Ben records 5 heads and 5 tails. They each tossed 10 times. Could both records be honest? Explain.
Unequal counts can occur with a fair coin.
Yes. Both total 10, and chance counts can differ. - A coin lands tails four times. Is tails impossible next time?
Earlier tosses do not remove a face.
No. Tails is still possible. - Two die experiments each have 12 rolls. One has 4 sixes; the other has 1 six. Find the difference.
4 − 1 = 3.
3 sixes. - Which statement recognises uncertainty: “I might get blue next” or “I must get blue next”?
Might allows more than one possible result.
“I might get blue next.” - A record has 9 heads and 1 tail in 10 tosses. Should it be changed to 5 and 5? Explain.
A surprising short run may happen; changing it would make the record inaccurate.
No. Keep the actual results. - Give possible counts for two imaginary ten-toss experiments. The head counts must differ, and each pair must total 10.
These are imagined examples, not invented records of a real experiment.
Check each pair totals 10 and the head counts differ.
For example, heads 3 and tails 7; heads 6 and tails 4. Many other pairs are valid.
Curriculum reference & lesson scope
Australian Curriculum v9 / South Australian Curriculum
Possible outcomes; likely/unlikely/certain/impossible; repeated experiments; variation.
Official curriculum source ↗