Understand the idea.
Keep the experiment the same
One trial is one turn of an experiment. Decide how many trials to carry out and what result to record before starting. Make one tally for each result, even if it surprises you, so every completed trial is counted once.
To repeat a bag experiment with unchanged contents, replace the selected counter and mix before choosing again without looking. Without replacement, the number or colours of counters change; later selections would then use a different bag from the first selection.
Expect variation
Equal chances describe the experiment, not a promise that short records will balance. A fair coin can give heads and tails in tosses. A fresh set of tosses can produce different counts while the coin stays the same.
A digital simulation can model a physical experiment when its possible outcomes and chances match the device. It should record the results it actually generates. Forcing every short run to have equal counts would remove variation that real chance trials can show.
| Outcome | Frequency |
|---|---|
| Heads | 12 |
| Tails | 8 |
See the method in action.
Check a trial record
An example record of 20 coin tosses shows 12 heads and 8 tails. Is its total correct, and must the coin be unfair?
| Outcome | Frequency |
|---|---|
| Heads | 12 |
| Tails | 8 |
Worked solution
- 1
Add the recorded heads and tails.
Each toss contributes to exactly one of the two frequencies, so their sum is the total recorded tosses.
- 2
Compare the total with the planned trials.
The recorded frequencies account for all twenty planned tosses, so the total is correct.
- 3
Assess what the unequal counts show.
A fair coin can produce unequal counts in twenty tosses; this short record alone does not prove that the coin is unfair.
The total is correct. The unequal counts do not prove unfairness.
Keep the bag unchanged
You want to repeat a colour selection 15 times using a bag with 3 red and 2 blue counters. How should each trial work?
Worked solution
- 1
Mix the counters and select one without looking.
Mixing and hiding the colours prevents deliberately choosing a preferred counter.
- 2
Record the selected colour once.
Every trial needs one record, including results that differ from the prediction.
- 3
Replace the counter and mix again.
Replacement restores three red and two blue counters, keeping the contents unchanged for the next selection.
- 4
Repeat until fifteen selections have been recorded.
Stopping at the planned number of trials avoids changing the length of the experiment to obtain a preferred result.
Select, record, replace and mix; repeat for 15 trials.
Try it yourself.
Check your understanding
A fair coin gives heads four times in a row. Is tails certain on toss five?
Show answer & reasoning
No.
No. On the fifth toss of the fair coin, heads and tails are still both possible with equal chances. Four earlier heads do not change the coin or make tails certain.
Keep practising
6 worksheet questions · 9 marks
Read the questions online
- What is one trial when testing a spinner?1 mark
- You plan 12 coin tosses. Your table shows 7 heads and 5 tails. Has every toss been counted?1 mark
- You plan 20 spins, but your table totals 19. What should you do?1 mark
- Why replace a selected counter before the next trial when repeating an unchanged bag experiment?1 mark
- Does the supplied example table prove that heads will occur more often in the next 20 tosses?2 marks
Example results from 20 tosses of a fair coin Outcome Frequency Heads 12 Tails 8 - Plan ten trials to compare a paper coin toss with a digital coin model. State how you will record results.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- What is one trial when testing a spinner?1 mark
A trial is a single repeat of the experiment.
One spin with one recorded outcome. - You plan 12 coin tosses. Your table shows 7 heads and 5 tails. Has every toss been counted?1 mark
.
The total is correct: 12. - You plan 20 spins, but your table totals 19. What should you do?1 mark
Do not invent a twentieth result.
Check the original tally for a missed or incorrectly counted trial. - Why replace a selected counter before the next trial when repeating an unchanged bag experiment?1 mark
Without replacement, the bag's contents change.
To restore the same numbers and colours of counters. - Does the supplied example table prove that heads will occur more often in the next 20 tosses?2 marks
Example results from 20 tosses of a fair coin Outcome Frequency Heads 12 Tails 8 The next set of trials may have different frequencies.
A fair coin gives the same chances on each new toss.
No. - Plan ten trials to compare a paper coin toss with a digital coin model. State how you will record results.3 marks
Choose the trial count first and record every result.
Compare the totals without expecting identical frequencies.
Toss a fair coin ten times and run a fair two-outcome digital model ten times. Use a separate heads/tails tally for each.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum 2026
Listing outcomes; equal/unequal likelihood; repeated trials; observed frequencies.
Official curriculum source ↗