Understand the idea.
Set up a repeatable trial
A trial is one repetition of a chance experiment: one coin toss or one draw from a bag. Decide the procedure and the number of trials before starting, so everyone knows what counts as one result.
For repeated bag draws with unchanged contents, return the drawn ball and mix after recording its colour. This resets the collection for the next trial. Keeping it out would change the experiment’s conditions.
Record what actually happens
Record every outcome once, either in trial order or with a tally for each outcome. Count unexpected results too. A record describes what actually happened, so changing it to match a prediction would make it unreliable.
For ten tosses showing only heads or tails, the two counts must add to ten. They need not be five each: a fair setup gives equal chances, while the results of a short experiment can vary.
| Trial | 1 | 2 | 3 | 4 | 5 | 6 | 7 | 8 | 9 | 10 |
|---|---|---|---|---|---|---|---|---|---|---|
| Result | H | T | H | H | T | T | H | T | H | H |
See the method in action.
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 |
Worked solution
- 1
Find all the heads in the record.
Reading each entry in order prevents a result from being missed or counted twice.
- 2
Count each outcome.
Six entries are H; the other four entries are T.
- 3
Check against the number of trials.
All ten recorded outcomes are accounted for, even though the counts are unequal.
6 heads and 4 tails.
A bag experiment
Write a rule for ten draws that keep the same bag contents each time.
Worked solution
- 1
Draw one equal-sized ball without looking.
A well-mixed, unseen draw avoids choosing a colour deliberately.
- 2
Record the colour once.
Each draw contributes exactly one outcome to the ten-trial record.
- 3
Return the ball and mix the bag.
Replacement restores the original contents, and mixing prepares the next random draw.
- 4
Repeat until ten draws have been recorded.
Using the same draw, record, replace and mix rule keeps the conditions the same for every trial.
Replace and mix after every recorded draw.
Try it yourself.
Check your understanding
Twenty trials produced eight red outcomes. If red and blue were the only options, how many were blue?
Show answer & reasoning
12.
Red and blue account for every trial, so subtract the 8 red outcomes from 20: blue outcomes. The check accounts for all trials.
Keep practising
6 worksheet questions · 10 marks
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
.
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 ↗