Compare the chance of events
Theory
Comparing the chance of events is a Year 4 chance skill: deciding whether one outcome is more likely, less likely or equally likely than another. This page shows how to compare a spinner's coloured parts and the counters in a bag, order colours from least to most likely, compare spinners by thinking about half, and decide whether a game is fair. Curriculum: VC2M4P01 / AC9M4P01.
The chance of an event is how likely it is to happen. To compare two colours on a spinner or in a bag, you count how much of each colour there is.
One colour is more likely when there is more of it — a bigger part on a spinner, or more counters in a bag. A colour is less likely when there is less of it. When there is the same amount of each colour, the two are equally likely. On a die, an event that can happen in more ways (such as rolling a number less than \(3\): \(1\) or \(2\)) is more likely than one that can happen in only one way (rolling a \(5\)).
A game is fair when every player has an equal chance of winning. If one player wins on more parts than another, the game is not fair. Remember that more likely does not mean certain — the other colour can still come up.
Comparing chance does not need a formula — just these facts.
You can also write a colour as a fraction of the whole. If a spinner has \(4\) equal parts and \(3\) are red, red covers \(\dfrac{3}{4}\) and blue covers \(\dfrac{1}{4}\), so red is more likely. Comparing with half helps when spinners have different numbers of parts.
How to compare the chance of two colours
- Count each colour. Count the equal parts of each colour on the spinner, or the counters of each colour in the bag.
- Compare the counts. The bigger count is more likely and the smaller count is less likely. Equal counts are equally likely.
- Different totals? Compare with half. If two spinners or bags have different totals, decide whether the colour is more than half, half or less than half of each one.
- Say the answer. Name the more likely colour, order the colours, or say whether a game is fair.
| \(\text{yellow}\) | \(=\) | \(4\text{ parts}\) |
| \(\text{purple}\) | \(=\) | \(2\text{ parts}\) |
| \(4\) | \(>\) | \(2\) |
Yellow has more parts, so yellow is more likely. Purple is less likely, but it can still come up.
| \(\text{green}\) | \(=\) | \(5\) |
| \(\text{yellow}\) | \(=\) | \(5\) |
| \(5\) | \(=\) | \(5\) |
The counts are the same, so green and yellow are equally likely.
| \(\text{Ava (red)}\) | \(=\) | \(3\text{ parts}\) |
| \(\text{Tom (blue)}\) | \(=\) | \(2\text{ parts}\) |
| \(3\) | \(>\) | \(2\) |
Ava has more parts, so the game is not fair. Colouring the parts \(2\) red, \(2\) blue and \(2\) green would give Ava and Tom the same chance.
| \(\text{yellow}\) | \(=\) | \(3\) |
| \(\text{green}\) | \(=\) | \(6\) |
| \(\text{blue}\) | \(=\) | \(10\) |
| \(3\) | \(<\) | \(6 < 10\) |
From least likely to most likely: yellow, green, blue.
Do not just count red parts, because the spinners have different numbers of parts. Ask: is red more than half, half, or less than half?
| \(\text{P: 2 of 6}\) | \(\text{less than half}\) | |
| \(\text{Q: 1 of 2}\) | \(\text{exactly half}\) |
Spinner Q gives the better chance of red.
(i) Which colour is more likely now?
(ii) \(5\) more red counters are put in. Which colour is more likely now?
| \(\text{before}\) | \(3\text{ red},\ 5\text{ blue}\) | |
| \(3 + 5\) | \(=\) | \(8\text{ red}\) |
| \(\text{after}\) | \(8\text{ red},\ 5\text{ blue}\) |
(i) Blue (\(5\) blue, \(3\) red).
(ii) Red (\(8\) red, \(5\) blue). Adding or taking away counters changes the chances.
\(8\) is half of \(16\). Blue covers \(5\) of the \(8\) parts, which is more than half the spinner.
Expect blue more than \(8\) times. It will not be exact every time, because chance results vary.
Common pitfalls
Frequently asked questions
What does more likely mean in maths?
An event is more likely when it has a bigger chance of happening. On a spinner it is the colour with the biggest part or the most equal parts, and in a bag it is the colour with the most counters.
How do you compare the chance of two colours?
Count how much of each colour there is. The colour with more parts on a spinner, or more counters in a bag, is more likely. If the amounts are the same, the two colours are equally likely.
What does equally likely mean?
Equally likely means two events have the same chance. A bag with \(6\) green and \(6\) yellow counters gives green and yellow an equal chance.
What is a fair game?
A game is fair when every player has an equal chance of winning. If one player wins on \(5\) parts and another wins on only \(3\) parts, the first player has a better chance, so the game is not fair.
Does more red always mean red will win?
No. More red only makes red more likely, not certain. The other colour can still come up, because chance is about what is likely, not what is guaranteed.
How do you find the least likely colour?
Find the colour with the smallest amount. In a bag with \(6\) green, \(3\) red and \(1\) blue counter, blue has the fewest, so blue is the least likely colour to be taken.