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Year 3 Maths Chance

List possible outcomes

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Theory

Listing the possible outcomes is a Year 3 chance skill: naming every different result of a simple chance experiment and counting them. This page covers the outcomes of a coin (heads or tails), a die (1 to 6), a colour spinner, letter cards and drawing a counter from a bag, and how to tell whether the outcomes are equally likely. Curriculum: VC2M3P01 / AC9M3P01.

A chance experiment is something with a result you cannot be sure of before it happens, like tossing a coin or rolling a die. An outcome is one result that could happen.

The possible outcomes are all the different results you could get. To find them, name each one, then count how many there are. A coin can land on heads or tails, so it has \(2\) outcomes. A standard die can show \(1, 2, 3, 4, 5\) or \(6\), so it has \(6\) outcomes.

For a spinner or a bag, there is one outcome for each different colour. Count the different results, not the objects: a bag of \(4\) green and \(2\) yellow counters still has only \(2\) colour outcomes. Outcomes are equally likely when each one has the same chance, such as the equal parts of a fair spinner.

A coin showing its two outcomes Two coins side by side: one shows heads with the letter H, the other shows tails with the letter T. A coin has two possible outcomes, heads and tails. H T heads tails
Coin: \(2\) outcomes — heads, tails.
A die showing its six outcomes Six die faces in a row showing one, two, three, four, five and six dots. A standard die has six possible outcomes, the numbers 1 to 6. 1 2 3 4 5 6
Die: \(6\) outcomes — \(1, 2, 3, 4, 5, 6\).
A colour spinner showing its five outcomes A spinner split into five equal parts coloured red, yellow, green, blue and purple, with an arrow. The spinner has five possible outcomes, one for each colour. RYGBP
Spinner: \(5\) outcomes — one for each colour.
A bag of counters showing its colour outcomes A bag holding four green counters and two yellow counters. Drawing one counter has two colour outcomes, green or yellow. G G G G Y Y
Bag: \(2\) colour outcomes — green, yellow.

Listing outcomes does not need formulas, but these common counts are worth remembering.

ExperimentPossible outcomesHow many
Toss a coinheads, tails2
Roll a die1, 2, 3, 4, 5, 66
Spinner with 3 coloursone per colour3
Spinner with 5 coloursone per colour5
Cards with different lettersone per letterone per card
Count the different results. A spinner or bag has one outcome for each colour, so \(3\) colours give \(3\) outcomes — even if the parts are different sizes or there are extra counters. Outcomes are equally likely only when every outcome has the same amount: equal parts on a spinner, or the same number of counters of each colour.

How to list all the possible outcomes

  1. Name the experiment. Work out what is happening: a coin toss, a die roll, a spin, a card or a draw from a bag.
  2. List each result. Write down every different thing that could happen, one at a time, and do not repeat any.
  3. Count them. Count how many results you listed. That number is how many possible outcomes there are.
  4. Check if they are equally likely. Equal parts or equal counts mean equally likely. A bigger part or more counters makes that outcome more likely.
Example 1 — Flip a counter
Ella flips a counter that is red on one side and yellow on the other. List all the outcomes, then count them.
Solution

The counter lands on one of its two sides.

\(\text{outcomes}\)\(=\)\(\text{red, yellow}\)
\(\text{count}\)\(=\)\(2\)

There are \(2\) possible outcomes. A coin works the same way: it has two faces.

Example 2 — Roll a number cube
A number cube has the numbers \(2, 4, 6, 8, 10\) and \(12\) on its six faces. List all the outcomes when you roll it. What is the smallest number you can roll, and the largest?
Solution

Write each number the cube can show.

\(\text{outcomes}\)\(=\)\(2, 4, 6, 8, 10, 12\)
\(\text{count}\)\(=\)\(6\)

There are \(6\) possible outcomes. The smallest is \(2\) and the largest is \(12\), so a number such as \(5\) or \(20\) can never be rolled. A standard die works the same way, with the numbers \(1\) to \(6\).

Example 3 — Colour spinner
A spinner has three equal parts: red, yellow and purple. List the outcomes, count them, and say whether they are equally likely.
A spinner with three equal parts: red, yellow and purple A spinner split into three equal parts coloured red, yellow and purple, with an arrow. RYP
Solution

The arrow can stop on each colour.

\(\text{outcomes}\)\(=\)\(\text{red, yellow, purple}\)
\(\text{count}\)\(=\)\(3\)

There are \(3\) possible outcomes. The parts are equal, so the three colours are equally likely.

Example 4 — Bag of counters
A bag has \(4\) red and \(3\) yellow counters. You draw one without looking. How many colour outcomes are there?
Solution

Count the different colours, not the counters.

\(\text{outcomes}\)\(=\)\(\text{red, yellow}\)
\(\text{count}\)\(=\)\(2\)

There are \(2\) colour outcomes.

Example 5 — Parts of different sizes
This spinner is half green, a quarter orange and a quarter purple. List the outcomes. Are they equally likely?
A spinner that is half green, a quarter orange and a quarter purple A spinner with a green half, an orange quarter and a purple quarter, with an arrow. GOP
Solution
\(\text{outcomes}\)\(=\)\(\text{green, orange, purple}\)
\(\text{count}\)\(=\)\(3\)

There are \(3\) outcomes, but they are not equally likely: the green part is bigger, so green is more likely than orange or purple.

Example 6 — Letter cards
The letters of the word FROG are written on \(4\) cards, one letter on each card. One card is picked without looking. List the possible outcomes.
Solution
\(\text{outcomes}\)\(=\)\(\text{F, R, O, G}\)
\(\text{count}\)\(=\)\(4\)

There are \(4\) possible outcomes, one for each different letter. Each card is equally likely to be picked.

Common pitfalls

Count colours, not counters. Watch out for counting every object. A bag with \(6\) green and \(1\) white counter has only \(2\) colour outcomes, not \(7\).
A die has no 0 and nothing above 6. The only outcomes are the numbers \(1\) to \(6\), so rolling a \(0\) or a \(9\) can never happen.
Different sizes do not change the list. A spinner with three colours has \(3\) outcomes even when one part is bigger. Size changes the chance, not the list.
Equal parts make outcomes equally likely. Only call outcomes equally likely when the parts are the same size or there are the same number of each colour.

Frequently asked questions

What are the possible outcomes of tossing a coin?

A coin can land on heads or tails. So there are two possible outcomes: heads and tails.

How many possible outcomes are there when you roll a standard die?

A standard six-sided die can show \(1, 2, 3, 4, 5\) or \(6\). That is six possible outcomes, and on a fair die they are all equally likely.

What is an outcome in maths?

An outcome is one result that could happen in a chance experiment. Tossing a coin has two outcomes, heads and tails.

How do you list all the possible outcomes?

Name every different result that could happen, one at a time, and then count how many you listed. For a colour spinner, list each colour the arrow can stop on.

Do you count the counters or the colours in a bag?

You count the different colours, not the counters. A bag with \(6\) green and \(1\) white counter has only two colour outcomes, green and white.

What does equally likely mean?

Equally likely means every outcome has the same chance. A spinner with equal parts in different colours gives every colour the same chance.

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