The idea, step by step
One repeat is a trial
One trial is one repeat of a chance action, such as one coin toss. Decide how many trials to make before starting. Record every result straight away, including results you did not expect.
If a bag experiment should stay the same each time, put the chosen counter back and mix before choosing again. Leaving it out changes the bag. A coin toss does not remove a face.
Use the real record
The frequencies tell how often outcomes happened in this experiment. Add them to check the trial total. Do not change the record to make it neater.
A fair coin need not give equal heads and tails in a short experiment. Repeat and compare before deciding whether equipment may be unfair.
| Outcome | Frequency |
|---|---|
| Heads | 11 |
| Tails | 9 |
A common trap
Erase an odd result so the experiment looks fair.
Instead: Keep every actual result. Fair procedures and honest records matter more than neat counts.
See the thinking
Check the number of trials
A record shows 11 heads and 9 tails. How many tosses were recorded?
- Add the two outcome counts.
- 11 + 9 = 20.
- Every toss belongs to one outcome in this flat-face record.
Keep the bag the same
A bag starts with 3 red and 1 blue counter. Why replace the chosen counter before each new trial?
- Leaving it out changes what remains.
- Putting it back restores the starting collection.
- Mixing prepares a new choice from that same collection.
Check your understanding
A record has 7 heads and 5 tails. How many tosses is that?
Show answer
12 tosses.
7 + 5 = 12.
Your turn
6 questions · Work at your own pace.
Read the questions online
- A die is rolled once. How many trials is that?
- A coin record contains 8 heads and 7 tails. Find the number of tosses.
- A class plans 20 tosses but records 12 heads and 6 tails. How many results are missing?
- A bag experiment should use the same collection each time. What two actions should follow reading a chosen counter?
- A die record has frequencies 2, 1, 3, 2, 2 and 2 for faces 1 to 6. Check the trial total and name the most frequent face.
- Toss a coin 10 times and record the counts, or use this sample: H, T, H, H, T, T, H, T, H, H. Give the head and tail counts.
Read the worked solutions
- A die is rolled once. How many trials is that?
One roll is one repeat of the action.
1 trial. - A coin record contains 8 heads and 7 tails. Find the number of tosses.
8 + 7 = 15.
15 tosses. - A class plans 20 tosses but records 12 heads and 6 tails. How many results are missing?
12 + 6 = 18.
20 − 18 = 2.
2 results. - A bag experiment should use the same collection each time. What two actions should follow reading a chosen counter?
This restores the setup and prepares another choice.
Put the counter back and mix the bag again. - A die record has frequencies 2, 1, 3, 2, 2 and 2 for faces 1 to 6. Check the trial total and name the most frequent face.
2 + 1 + 3 + 2 + 2 + 2 = 12.
12 trials; face 3 with 3 results. - Toss a coin 10 times and record the counts, or use this sample: H, T, H, H, T, T, H, T, H, H. Give the head and tail counts.
Count every result once.
For the sample, 6 + 4 = 10.
Sample: heads 6, tails 4. Actual experiment counts may differ but must total 10.
Curriculum reference & lesson scope
Australian Curriculum v9 / South Australian Curriculum
Possible outcomes; likely/unlikely/certain/impossible; repeated experiments; variation.
Official curriculum source ↗