The idea, step by step
Keep the experiment the same
A trial is one turn of a chance experiment, such as tossing a coin or spinning a spinner. Decide the number of trials before starting. Record each result once in a tally or table, including results that do not match your prediction.
When selecting a counter from a bag, put it back and mix before the next trial if you want the bag's contents to remain the same. If you do not replace it, you have changed the experiment.
Expect variation
Equal chances do not promise equal counts in a short experiment. A fair coin could give 12 heads and 8 tails in 20 tosses. Repeating the 20 tosses may give different counts, and that alone does not show the coin has changed.
A paper device and a digital simulation can model the same experiment if their outcomes and chances match. A simulation should record its actual results, not be programmed to force equal counts.
| Outcome | Frequency |
|---|---|
| Heads | 12 |
| Tails | 8 |
A common trap
After several heads, tails must be next so the results can balance.
Instead: For a fair coin, each new toss still gives heads and tails equal chances. Earlier results do not force the next one.
See the thinking
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 |
- Add the two frequencies: 12 + 8 = 20.
- The total matches the planned number of trials.
- A difference can occur by chance. These results alone do not prove the coin is unfair.
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?
- Mix and choose one counter without looking.
- Record its colour.
- Return the counter and mix again before the next selection.
Check your understanding
A fair coin gives heads four times in a row. Is tails certain on toss five?
Show answer
No.
The fifth toss can still be heads or tails; earlier tosses do not make tails certain.
Your turn
6 questions · 9 marks · Work at your own pace.
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
7 + 5 = 12.
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 ↗