Understand the idea.
Same setup, different counts
Variation means that chance results can differ. Two children can each toss the same fair coin ten times and get different numbers of heads. They could also get matching counts; neither kind of record is promised.
A fair coin does not remember earlier tosses. After several heads, heads and tails are still possible on the next flat-face landing. Tails does not become compulsory to make the earlier counts balance.
Describe what happened
Compare the numbers of trials as well as the results. When two experiments both have ten tosses, you can directly compare their head counts. Say what happened in those experiments, using the actual counts as evidence.
A record describes past results, not a promise about the next one. More trials give more information about an experiment, but do not make its next result certain. A short uneven run alone does not prove unfair equipment.
| Child | Heads | Tails |
|---|---|---|
| Ella | 7 | 3 |
| Noah | 4 | 6 |
See the method in action.
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?
Worked solution
- 1
Check the experiment sizes.
They made the same number of tosses, so we are comparing two head counts from equal-sized experiments.
- 2
Find the difference in heads.
Ella recorded three more heads than Noah.
- 3
Explain whether the difference shows an error.
Chance can give different counts under the same setup. The difference alone does not make Noah's record wrong; both could be correct.
Ella has 3 more heads. Both records could be correct.
What happens next?
A fair coin gives heads three times in a row. Must the next result be tails?
Worked solution
- 1
Identify what can happen on the next toss.
The fair coin still has its head and tail faces, so either flat-face result remains possible.
- 2
Check whether the earlier tosses change that choice.
Three heads do not remove the head face or make tails compulsory. The coin's next toss is not controlled by the earlier results.
- 3
Answer the word must.
No: tails could happen next, but heads could happen again. Neither result is certain.
No. Heads or tails can happen next.
Try it yourself.
Check your understanding
Two groups each toss a fair coin 8 times. Must their head counts match?
Show answer & reasoning
No.
The head counts need not match. Even with fair coins and eight tosses each, chance can give the groups different results.
Keep practising
6 worksheet questions
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.
.
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 ↗