The idea, step by step
Set up a repeatable trial
One trial is one repeat of the experiment, such as one coin toss or one draw from a bag. Decide the rule before starting. For a bag experiment, say whether the ball is replaced. To compare repeated draws under the same conditions, return the ball and mix after each draw.
Record what actually happens
List outcomes in order or tally their frequencies. Count every trial once, including unexpected outcomes. After ten coin tosses, heads and tails counts must add to ten. The results do not have to be five of each. Never edit a record to make it look fair.
| Trial | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Result | H | T | H | H | T | T | H | T | H | H |
A common trap
Changing an unusual result because it does not fit the prediction.
Instead: Record the actual result. Chance variation is part of the experiment.
See the thinking
Count a supplied record
Use the supplied ten-toss record to count heads and tails.
| Trial | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Result | H | T | H | H | T | T | H | T | H | H |
- Heads occur on trials 1, 3, 4, 7, 9 and 10: six heads.
- The other four trials are tails.
- 6 + 4 = 10, so the count checks.
A bag experiment
Write a rule for ten draws that keep the same bag contents each time.
- Draw one equal-sized ball without looking.
- Record its colour.
- Return it, mix, and repeat until ten trials are recorded.
Check your understanding
Twenty trials produced eight red outcomes. If red and blue were the only options, how many were blue?
Show answer
12.
20 − 8 = 12, so the total remains twenty.
Your turn
6 questions · 10 marks · Work at your own pace.
Read the questions online
- In a coin experiment, what could count as one trial?1 mark
- Count heads in H, T, H, T, T, H, H, T.1 mark
- Eight trials give three red results and only red/blue outcomes. How many results are blue?1 mark
- Why should a counter be replaced in every trial if the aim is to keep bag contents unchanged?2 marks
- A learner tosses a coin ten times but records only nine results. What should the learner do?2 marks
- Plan a twelve-trial bag experiment. State the setup, trial rule and recording method.3 marks
Read the worked solutions
Equivalent correct methods earn the corresponding marks. Include units where asked.
- In a coin experiment, what could count as one trial?1 mark
Each repeat has one recorded outcome.
One toss of the coin. - Count heads in H, T, H, T, T, H, H, T.1 mark
Heads occur in positions 1, 3, 6 and 7.
4 heads. - Eight trials give three red results and only red/blue outcomes. How many results are blue?1 mark
8 − 3 = 5.
5. - Why should a counter be replaced in every trial if the aim is to keep bag contents unchanged?2 marks
Without it, later trials use different contents.
Replacement restores the starting collection. - A learner tosses a coin ten times but records only nine results. What should the learner do?2 marks
Do not invent an outcome to fill the gap.
Check the record and report the missing result honestly; repeat the planned experiment if necessary. - Plan a twelve-trial bag experiment. State the setup, trial rule and recording method.3 marks
Other clear fair setups are valid when the same rule is followed.
For example: use 2 red and 2 blue equal counters, draw without looking, record colour, replace and mix, repeat 12 times in a tally table.
Curriculum reference & lesson scope
Australian Curriculum v9 / SA Curriculum Mathematics 2026
Ordering likelihood; independent/dependent events; repeated trials; comparing variation.
Official curriculum source ↗