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Year 5 Maths Chance

List outcomes of chance experiments

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Theory

A chance experiment is something with an uncertain result, like rolling a die. Each possible result is an outcome. This Year 5 maths page shows how to list every outcome, how to list the outcomes in an event, and how to tell if outcomes are equally likely.

An outcome is one possible result. Tossing a coin has \(2\) outcomes (heads, tails); rolling a die has \(6\) (\(1\) to \(6\)).

An event is a group of outcomes. On a die, the event "a number greater than \(2\)" is made of the outcomes \(3, 4, 5, 6\).

Outcomes are equally likely when each has the same chance: equal sectors on a spinner, or one of each item in a bag. Bigger sectors or more counters of one colour make that outcome more likely.

When drawing from cards or counters, list each different result once: the letters of KOALA give \(4\) outcomes (K, O, A, L), because A appears twice.

For two steps (a coin then a spinner), list every pair in a table or tree so none is missed.

Spinner with three red sectors A spinner with six equal sectors: red, blue, red, green, red and blue. Red Blue Red Green Red Blue
Outcomes: red, blue, green (\(3\)). Red is most likely: it has \(3\) of the \(6\) sectors.
Coin and spinner outcomes A table with rows H and T for the coin and columns 1, 2 and 3 for a three-part spinner. The cells read H1, H2, H3, T1, T2, T3. Spinner 123 H H1 H2 H3 T T1 T2 T3 Coin
A coin and a \(1\)-\(2\)-\(3\) spinner: \(2 \times 3 = 6\) outcomes.

Common experiments:

ExperimentOutcomesNumber
Toss a coinH, T\(2\)
Roll a die\(1, 2, 3, 4, 5, 6\)\(6\)
Spin a spinner with \(5\) equal sectors A to EA, B, C, D, E\(5\)
Toss a coin and spin \(1\)-\(2\)-\(3\)H1, H2, H3, T1, T2, T3\(6\)
Outcomes, not events. "Even" is an event made of the outcomes \(2, 4, 6\).
Different results only. Two red sectors still give only one outcome: red.

Listing outcomes

  1. Ask: what could happen after one go?
  2. List each different result once.
  3. For two steps, pair every first result with every second result (table or tree).
  4. For an event, pick out the outcomes that fit the description.
Example 1 — List outcomes
A spinner has \(5\) equal sectors labelled A, B, C, D and E. List the outcomes.
Solution

A, B, C, D, E: \(5\) outcomes, all equally likely.

Example 2 — Event on a die
A die is rolled. List the outcomes in each event.
(i) A number greater than \(2\)
(ii) A factor of \(6\)
Solution

(i) \(3, 4, 5, 6\)
(ii) \(1, 2, 3, 6\)

Example 3 — Repeated letters
The letters of KOALA are on five cards. One card is drawn. List the different outcomes.
Solution

K, O, A, L: \(4\) different outcomes. A is more likely than the others because there are two A cards.

Example 4 — Equally likely?
Use the first diagram.
(i) List the outcomes.
(ii) Are they equally likely?
Solution

(i) Red, blue, green
(ii) No. Red has \(3\) of the \(6\) sectors, blue \(2\) and green only \(1\).

Example 5 — Bag of counters
A bag has \(4\) yellow and \(4\) purple counters. One is drawn.
(i) How many outcomes are there?
(ii) Are they equally likely?
Solution

(i) \(2\): yellow, purple
(ii) Yes, there are the same number of each.

Example 6 — Two steps
A coin is tossed and a spinner numbered \(1\), \(2\), \(3\) is spun. List all the outcomes.
Solution
\(2 \times 3\)\(=\)\(6\)
2×3=6

H1, H2, H3, T1, T2, T3 (see the second diagram).

Example 7 — Count an event
In the coin-and-spinner experiment, how many outcomes have a head and an odd number?
Solution

\(2\): H1 and H3.

Example 8 — Find the mistake
Ben says a spinner with sectors red, red, blue has \(3\) outcomes. What is right?
Solution

There are only \(2\) different outcomes, red and blue. Red is more likely.

Common pitfalls

Confusing events with outcomes. "Odd" is not an outcome; \(1\), \(3\), \(5\) are.
Listing repeats. List each different result once.
Assuming equally likely. Check the sizes of the sectors or the numbers of each item.
Missing pairs in two steps. Use a table or tree to list them all.

Frequently asked questions

What is an outcome?

One possible result of a chance experiment.

How many outcomes when you roll a die?

\(6\): \(1, 2, 3, 4, 5, 6\).

What is an event?

A group of outcomes, like "an even number" (\(2, 4, 6\)).

When are outcomes equally likely?

When each has the same chance, like equal sectors on a spinner.

How do I list outcomes for two steps?

Draw a table or tree that pairs each first result with each second result.

More in Chance
Repeated chance experiments: record & compare frequencies
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