Conducting single-stage experiments | Year 7

01 / LEARN

The idea, step by step

Choose the rules before starting

A useful experiment has a clear question and repeatable trial. For a coin, write “toss once, let it land, record the upper face”. Choose the number of trials in advance. Agree what to do about an edge landing or a coin outside the tray.

Record results as they happen, using a tally or frequency table. Include one row for each possible result. Stop at the planned number of valid trials, not as soon as a preferred pattern appears.

Keep the model unchanged and report honestly

For repeated bag draws meant to keep the same colour probabilities, return each counter after recording it, then mix again. Without replacement, the bag contents change. Keep the spinner and the boundary rule unchanged for repeated spinner trials.

Check that frequencies sum to the number of valid trials. Compare with the expected count and describe differences. A short experiment can suggest more testing, but an unbalanced record alone does not prove a device fair or unfair.

Example record of 20 coin tosses
Result	Frequency
Heads	12
Tails	8

A common trap

Stopping as soon as the results look balanced.

Instead: Choose the trial count before starting. Stopping because of the outcomes makes the result depend on a changing stopping rule.

02 / WORKED EXAMPLES

See the thinking

Example 1

Check an experimental record

Use the coin table. Find the number of trials and how far the heads count is above the fair-coin expectation.

Example record of 20 coin tosses
Result	Frequency
Heads	12
Tails	8

Add the counts: $12 + 8 = 20$ .
Expected heads for a fair coin: $20 \times 1 / 2 = 10$ .
Observed heads exceed expectation by $12 - 10 = 2$ .

20 trials; heads are 2 above expectation.

Example 2

Improve a repeated bag experiment

A student removes counters after each draw but uses the original colour probability every time. How should they change the procedure to keep that probability unchanged?

Removing counters changes the contents.
Return each counter after recording its colour.
Mix again and choose without looking.

Replace and remix the counter after every draw.

Check your understanding

A 30-trial table contains frequencies 8, 11 and 10. What needs checking?

Show answer

One trial is missing or a count is incorrect.

The counts sum to 29, not 30. Check the original record rather than inventing a result.

03 / WORKSHEET

Your turn

6 questions · 16 marks · Work at your own pace.

Worksheet PDF Worked solutions

Read the questions online

Describe one trial when testing the colour results of a spinner.
2 marks
An experiment records 9 red, 7 blue and 8 green results. How many valid trials are recorded?
2 marks
Why should a counter be returned and the bag remixed when each draw is meant to have the original probabilities?
3 marks
Use the coin table. State the observed and fair-model expected tails counts.
2 marks
Example record of 20 coin tosses
Result Frequency
Heads 12
Tails 8
A student only records heads and ignores tails. Explain why the record is incomplete.
3 marks
Plan 40 draws from a bag of 2 red and 3 blue equal-size counters. Include selection, replacement, recording and expected reds.
4 marks

Read the worked solutions

Equivalent correct methods earn the corresponding marks. Include units where asked.

Describe one trial when testing the colour results of a spinner.
2 marks
State both the action and the recorded result.
Choose a boundary rule in advance.
Spin once and record the colour where the pointer stops.
An experiment records 9 red, 7 blue and 8 green results. How many valid trials are recorded?
2 marks
Add every frequency: $9 + 7 + 8 = 24$ .
24.
Why should a counter be returned and the bag remixed when each draw is meant to have the original probabilities?
3 marks
Replacement restores the numbers of each colour.
Mix and choose without looking to avoid deliberate selection.
Returning restores the contents; remixing helps keep selection random.
Use the coin table. State the observed and fair-model expected tails counts.
2 marks
Example record of 20 coin tosses
Result Frequency
Heads 12
Tails 8
Read 8 tails from the table.
Expected tails are $20 \times 1 / 2 = 10$ .
8 observed; 10 expected.
A student only records heads and ignores tails. Explain why the record is incomplete.
3 marks
Every valid trial must be recorded.
Ignoring results prevents a valid comparison of heads with all tosses.
You cannot check the total trials or the tails count.
Plan 40 draws from a bag of 2 red and 3 blue equal-size counters. Include selection, replacement, recording and expected reds.
4 marks
Returning maintains red chance $2 / 5$ .
All recorded frequencies should total 40.
$40 \times 2 / 5 = 16$ .
Draw without looking; record colour; replace and mix; repeat for 40 valid draws; expect 16 red.

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Curriculum reference & lesson scope

Australian Curriculum v9 and SA Curriculum Mathematics

Year 7 single-stage sample spaces, equally likely outcomes, probabilities, expected frequencies, chance experiments, simulations and relative frequencies.

Official curriculum source ↗

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