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Year 3 Maths Chance

Describe the chance of events

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Theory

Describing the chance of events is a Year 3 chance skill: deciding how likely something is and naming it with a chance word. This page explains the five words — impossible, unlikely, even chance, likely and certain — how to order them on a chance line, how they match will happen, might happen and won't happen, and how to use spinners, dice, coins and bags of counters to decide which outcome is more likely. Curriculum: VC2M3P01 / AC9M3P01.

The chance of an event tells us how likely it is to happen. We describe it with words, not numbers. There are five main chance words, and they go in order from least likely to most likely.

Impossible means it can never happen (it won't happen). Unlikely means it probably will not happen, but it could. Even chance means it is just as easy to happen as not, so the two outcomes are equally likely. Likely means it will probably happen, but is not sure. Certain means it must happen (it will happen). Unlikely, even chance and likely events all might happen.

These words sit on a chance line that runs from impossible on the left to certain on the right. An even chance sits right in the middle. Tossing a fair coin is a good example of an even chance, because heads and tails are equally likely.

The chance line from impossible to certain A horizontal chance line with five marks labelled impossible, unlikely, even chance, likely and certain. Events are placed above: rolling a 0 on a die at impossible, rolling a 1, 2 or 3 at even chance, and Monday coming after Sunday at certain. impossible unlikely even chance likely certain roll a 0on a die roll 1, 2or 3 Monday comesafter Sunday
The chance line: events go from impossible on the left to certain on the right.
A spinner with three yellow parts and three green parts A round spinner split into six equal parts, three yellow and three green, with an arrow. Landing on yellow is an even chance because half of the spinner is yellow. YGYGYG
Half of the parts are yellow: landing on yellow is an even chance.

Chance does not use numbers in Year 3, but these facts help you pick the right word. The five chance words always go in this order:

\[ \text{impossible} \to \text{unlikely} \to \text{even chance} \to \text{likely} \to \text{certain} \]
impossibleunlikelyevenchancelikelycertain

An event that will happen is certain, one that won't happen is impossible, and one that might happen is somewhere in between. An even chance sits in the middle, where the two outcomes are equally likely, like half the parts of a spinner being one colour.

\[ \text{even chance} = \text{half the parts} \]
evenchance=halftheparts
More parts, more chance. On a spinner or in a bag, the colour with more equal parts or more counters is more likely. More than half means likely; less than half means unlikely. If every part is the same colour, that colour is certain and any other colour is impossible.

How to describe the chance of an event

  1. Ask if it must happen. If the event is sure to happen every time, it is certain.
  2. Ask if it can never happen. If there is no way for it to happen, it is impossible.
  3. Decide in between. If it might happen, compare the ways it can happen with the ways it cannot. Fewer than half the ways is unlikely, exactly half is an even chance, and more than half is likely.
Example 1 — Certain event
You roll a normal die with the numbers \(1\) to \(6\). Describe the chance of rolling a number less than \(10\).
Solution

Every number on the die is \(1,\ 2,\ 3,\ 4,\ 5\) or \(6\). All of them are less than \(10\), so it must happen.

The chance is certain. It will happen.

Example 2 — Impossible event
A spinner has only red parts and blue parts. Describe the chance of the arrow landing on green.
Solution

There is no green part on the spinner, so there is no way for the arrow to land on green.

The chance is impossible. It won't happen.

Example 3 — Unlikely spinner
The spinner has four equal parts. One is red and three are blue. Describe the chance of landing on red.
A spinner with one red part and three blue parts A round spinner split into four equal quarters. One quarter is red and three quarters are blue, with an arrow. Landing on red is unlikely because only a small part is red. RBBB
Solution

Red is only \(1\) of the \(4\) equal parts, which is less than half of the spinner, but it is there.

So landing on red is unlikely. It might happen, but probably will not.

Example 4 — Which is more likely?
On a normal die, which is more likely: rolling a \(1\), or rolling a number bigger than \(1\)?
Solution

Rolling a \(1\) can happen only one way. A number bigger than \(1\) can be \(2,\ 3,\ 4,\ 5\) or \(6\), which is five ways.

Rolling a number bigger than \(1\) is more likely. It is likely, and rolling a \(1\) is unlikely.

Example 5 — Most likely colour
A jar holds \(7\) green, \(2\) yellow and \(1\) red counter. You take one without looking.
(i) Which colour are you most likely to take?
(ii) Which colour is least likely?
(iii) Describe the chance of taking a blue counter.
A jar of 7 green, 2 yellow and 1 red counter A container holding 7 green counters, 2 yellow counters and 1 red counter. G G G G G G G Y Y R
Solution

Compare the counts: green \(7\), yellow \(2\), red \(1\). There are no blue counters.

(i) Green, because there are the most green counters.
(ii) Red, because there is only \(1\).
(iii) Impossible.

Example 6 — Design a spinner
A spinner has \(6\) equal parts. Each part is coloured blue or white.
(i) How many parts should be blue so that blue is certain?
(ii) How many so that blue is impossible?
(iii) How many so that blue is an even chance?
Solution

Certain means every part is blue. Impossible means no part is blue. Even chance means half the parts are blue.

\(\text{certain}\)\(6\text{ blue parts}\)
\(\text{impossible}\)\(0\text{ blue parts}\)
\(\text{even chance}\)\(3\text{ blue},\ 3\text{ white}\)

(i) \(6\).
(ii) \(0\).
(iii) \(3\), because \(3\) is half of \(6\).

Example 7 — Compare two bags
Bag A has \(3\) red and \(7\) blue counters. Bag B has \(6\) red and \(4\) blue counters. From which bag are you more likely to take a red counter?
Solution

Both bags have \(10\) counters. Bag A has \(3\) red, which is less than half. Bag B has \(6\) red, which is more than half.

You are more likely to take red from Bag B.

Common pitfalls

Even chance does not mean it will happen. Watch out for thinking an even chance is a promise. It just means the event is as easy to happen as not.
Unlikely is not impossible. An unlikely event can still happen. Rolling a \(6\) is unlikely, but it does happen sometimes.
Certain and likely are not the same. A certain event must happen every time, but a likely event only probably happens.
Look at all the parts. Count every equal part of a spinner or every counter in a bag before you choose a word. A colour with more parts is more likely.

Frequently asked questions

What are the five chance words?

The five chance words are impossible, unlikely, even chance, likely and certain. They go in order on a chance line from impossible on the left to certain on the right.

What does even chance mean?

Even chance means an event is just as easy to happen as not to happen. The two outcomes are equally likely, like half of a spinner being red.

What is the difference between unlikely and impossible?

An impossible event can never happen. An unlikely event can still happen, it just does not happen very often.

How do you describe the chance of an event?

Ask if the event must happen, can never happen, or is somewhere in between. If it must happen it is certain, if it can never happen it is impossible, and in between it is unlikely, an even chance, or likely.

Is rolling a 6 on a die likely or unlikely?

Rolling a \(6\) is unlikely. A die has six numbers and only one of them is a \(6\), so it does not happen very often.

What does certain mean in maths?

Certain means the event must happen. It is sure to happen every time, like a day ending at midnight.

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