Chance experiments: record results & variation
Theory
Chance experiments are a Year 3 chance skill: tossing coins, rolling dice and spinning spinners many times and recording the results. This page shows how to record results in a list, tally, table or column graph, read and count them, find a missing result, compare results with a prediction, and explain why results vary each time the experiment is repeated. Curriculum: VC2M3P02 / AC9M3P02.
A chance experiment is something you can repeat where the result depends on chance, like tossing a coin, rolling a die, spinning a spinner or drawing a counter from a bag (and putting it back). Each go is called a trial.
You record every result as you go, in a list, a tally or a table. Then you count how many times each result came up, and you can show the counts in a column graph. The counts should add up to the number of trials.
Results vary: if you do the same experiment again, you usually get different results. Equally likely outcomes come up about the same number of times, but rarely exactly. A prediction says what you think is likely to happen; the results may be close to it without matching it exactly.
Recording a chance experiment uses the same counting skills as any data. These facts help you think about the results.
How to run and record a chance experiment
- Decide what to do and how many times. For example, toss a coin \(20\) times, or spin a spinner \(12\) times.
- Predict. Think about which result is likely to come up more often, and why.
- Record every result. Use a list, a tally or a table. Make one mark for each result.
- Count and display. Count each result, check the counts add to the total, and draw a table or column graph.
- Talk about the results. Compare them with your prediction. There is nearly always some variation: results are rarely exactly what you predicted.
Go through the list one result at a time and make one tally mark for each. Cross off each result as you go.
| \(\text{red}\) | \(=\) | \(5\) |
| \(\text{blue}\) | \(=\) | \(5 + 2 = 7\) |
| \(5 + 7\) | \(=\) | \(12\) |
Red came up \(5\) times and blue \(7\) times. The counts add to \(12\), so every spin was recorded.
(i) How many times did he roll a \(6\)?
(ii) Which number did not come up? Is that surprising?
| \(\text{sixes}\) | \(=\) | \(4\) |
| \(\text{missing number}\) | \(=\) | \(5\) |
(i) \(4\) times (the 1st, 4th, 7th and 10th rolls).
(ii) \(5\) did not come up. That is not surprising: with only \(12\) rolls, some numbers can come up a lot and others not at all, just by chance.
(i) Which colour came up most often?
(ii) How many spins were not blue?
| Colour | Number of times |
|---|---|
| Red | 4 |
| Blue | 6 |
| Yellow | 5 |
| \(4 + 6 + 5\) | \(=\) | \(15\) |
| \(4 + 5\) | \(=\) | \(9\) |
(i) Blue (\(6\) times).
(ii) \(9\) spins (red and yellow together). The colours are equally likely, but the counts are not exactly the same — that is normal.
| \(\text{tails}\) | \(=\) | \(9\) |
| \(9 - 7\) | \(=\) | \(2\) |
Tails came up \(9\) times, \(2\) more than heads. Check: \(7 + 9 = 16\) tosses.
| \(18 - 10\) | \(=\) | \(8\) |
| \(10\) | \(>\) | \(8\) |
Blue came up \(8\) times, so red came up more often in this experiment.
Each toss is up to chance, so it can land either way, no matter what happened before.
No. Doing the same experiment can give different results each time. This is called variation. Both results are possible with a fair coin.
| \(\text{half of }30\) | \(=\) | \(15\) |
| \(17 - 15\) | \(=\) | \(2\) |
No. Heads and tails are equally likely, but the results do not have to be exactly \(15\) and \(15\). Being a few away from half is normal variation, not a sign the coin is unfair.
| \(7 + 5 + 3\) | \(=\) | \(15\) |
| \(10 + 10 + 10\) | \(=\) | \(30\text{ tosses}\) |
\(15\) heads in \(30\) tosses, which is half. Each group's result was different, but putting all the results together gave a total close to half.
(i) Was her prediction right?
(ii) If she spins \(18\) more times, will she get exactly \(15\) greens again?
(i) Yes: \(15\) is more than \(3\). Green covers more of the spinner, so it is likely to come up more often.
(ii) Not for sure. Green is still likely, but the exact results change by chance each time.
Common pitfalls
Frequently asked questions
What is a chance experiment?
A chance experiment is something you can repeat where the result depends on chance, such as tossing a coin, rolling a die or spinning a spinner.
How do you record the results of a chance experiment?
Make a mark for every result as it happens, using a list, a tally or a table. Then count each result and check that the counts add up to the number of trials.
Why do results change each time?
Each toss, roll or spin is up to chance, so the results are different each time you repeat the experiment. This is called variation.
If a coin is fair, will I get exactly half heads?
Not always. You will usually get about half heads, but often a few more or a few fewer. That is normal variation.
In 6 tosses, is all tails or a mix of heads and tails more likely?
A mix is much more likely. All tails can happen in only one way: every one of the 6 tosses must be tails. A mix can happen in lots of ways, such as heads first, or tails first, or heads in the middle, so a mix comes up far more often.
Is a 6 harder to roll than a 1?
No. A fair die has one face for each number, so every number from \(1\) to \(6\) has the same chance.