Understand the idea.
One repeat is a trial
A trial is one go at a chance action, such as one toss or one roll. Decide the number of trials first. Record each result immediately so a surprising outcome is not forgotten or counted twice.
Keep the setup the same when you want repeated trials under the same conditions. After drawing and recording a counter, put it back and mix again. Leaving it out changes which counters are available next time.
Use the real record
Frequency tells how many times an outcome happened in your experiment. Add all outcome frequencies to check the number of recorded trials. If the total is wrong, recheck the record instead of inventing a missing result.
Fair equipment can produce uneven counts in a short experiment. Keep the results that actually occurred, even if heads and tails differ. More experiments provide more evidence; one short uneven record does not prove that a coin is unfair.
| Outcome | Frequency |
|---|---|
| Heads | 11 |
| Tails | 9 |
See the method in action.
Check the number of trials
A record shows 11 heads and 9 tails. How many tosses were recorded?
Worked solution
- 1
Identify the two recorded outcome counts.
Each recorded toss appears in one of these two groups, not both.
- 2
Add the frequencies.
Combining the two groups counts every recorded toss once.
- 3
Name the trial total.
One coin toss is one trial, so the record contains twenty trials.
20 tosses.
Keep the bag the same
A bag starts with 3 red and 1 blue counter. Why replace the chosen counter before each new trial?
Worked solution
- 1
Identify the starting collection.
These colour counts describe the bag we want to use for every trial.
- 2
Put the chosen counter back after recording it.
Replacement restores all four original counters; leaving one out would change the collection.
- 3
Mix before the next choice.
Mixing prepares another choice from the restored collection rather than leaving the returned counter in a known place.
To keep the same bag contents for every trial.
Try it yourself.
Check your understanding
A record has 7 heads and 5 tails. How many tosses is that?
Show answer & reasoning
12 tosses.
Each recorded toss is either a head or a tail in this record. Adding the counts gives tosses.
Keep practising
6 worksheet questions
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 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.
.
15 tosses. - A class plans 20 tosses but records 12 heads and 6 tails. How many results are missing?
.
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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 for faces 1 to 6. Check the trial total and name the most frequent face.
.
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, .
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 ↗