New
New
Year 9

Comparing representations of outcomes for more than two events

I can identify the same outcome across all the different representations.

New
New
Year 9

Comparing representations of outcomes for more than two events

I can identify the same outcome across all the different representations.

Lesson details

Key learning points

  1. Fluency in moving between the representations is important.
  2. Sometimes it is better to display the outcomes using a particular representation.

Common misconception

I can use outcome tables to categorise outcomes into as many events as I want.

Outcome tables are limited to categorising outcomes into only two events. You can use more tables to categorise outcomes into three or more events, but the number of tables you need quickly becomes massive!

Keywords

  • Outcome table - An outcome table is a table that shows all the possible outcomes.

  • Tree diagram - Tree diagrams are a representation used to model statistical/probability questions. Branches represent different possible events or outcomes.

  • Outcome tree - Each branch of an outcome tree shows a possible outcome from an event or from a stage of a trial. The full outcome tree shows all possible outcomes.

  • Venn diagram - Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.

Whilst it is possible to use Venn diagrams to categorise outcomes into four events, the layout of the four circles (they must be ellipses rather than specifically circles) is impractical for students to recreate and use. Therefore, we limit the number of events we work with to a maximum of three.
Teacher tip

Licence

This content is © Oak National Academy Limited (2024), licensed on Open Government Licence version 3.0 except where otherwise stated. See Oak's terms & conditions (Collection 2).

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6 Questions

Q1.
The Venn diagram shows the sample space $$\xi$$ = {2, 7, 77, 104}. Match each region to the correct outcome.
An image in a quiz
Correct Answer:Region a,104

104

Correct Answer:Region b,2

2

Correct Answer:Region c,7

7

Correct Answer:Region d,77

77

Q2.
The Venn diagram shows a selection of sports that Alex and Laura do and do not like. Which of these statements is true?
An image in a quiz
Both Alex and Laura like cricket.
Alex likes cricket, but Laura does not like cricket.
Correct answer: Alex does not like cricket, but Laura likes cricket.
Neither Alex nor Laura like cricket.
Q3.
This incomplete outcome tree represents all outcomes from spinning spinner X twice and subtracting the outcome of spin 2 from spin 1. Match each letter to its value in the sample space
An image in a quiz
Correct Answer:a,-2

-2

Correct Answer:b,10

10

Correct Answer:c,9

9

Correct Answer:d,3

3

Correct Answer:e,-7

-7

Q4.
Trial: spinning this spinner once. Event: factor of 120. This event and its opposite event are represented on an outcome tree. Which outcome should be written inside the box?
An image in a quiz
1
3
5
Correct answer: 7
8
Q5.
Trial: Spinner A is spun twice and coin is flipped. The outcome of each spin is added together. This incomplete outcome tree shows all the trial's outcomes. Match each letter on the tree to its value.
An image in a quiz
Correct Answer:a,48

48

Correct Answer:b,12

12

Correct Answer:c,72

72

Correct Answer:d,18

18

Q6.
Both the Venn diagram and outcome tree represent the same two events from a trial. Match the outcome from the Venn diagram to the missing outcome from the outcome tree.
An image in a quiz
Correct Answer:a,60

60

Correct Answer:b,45

45

Correct Answer:c,100

100

Correct Answer:d,177

177

6 Questions

Q1.
Which of these statements is true?
An outcome table can be used to list the outcomes of a three-stage trial.
An outcome table can categorise the outcomes of a trial into three events.
A Venn diagram can be used to list the outcomes of a three-stage trial.
Correct answer: A Venn diagram can categorise the outcomes of a trial into three events.
Correct answer: An outcome tree can be used to list the outcomes of a three-stage trial.
Q2.
Lucas creates an outcome tree to systematically list all possible three-course meals. The 1st layer of branches will show the starters. The number of branches needed for the 1st layer is .
An image in a quiz
Correct Answer: 4, 4 branches, four, four branches
Q3.
Lucas creates an outcome tree to systematically list all possible three-course meals. The 2nd layer of branches will show the mains. The number of branches needed in total for the 2nd layer is .
An image in a quiz
Correct Answer: 20, 20 branches, twenty, twenty bracnches
Q4.
This is an incomplete list of outcomes to a three-stage trial. Match each statement to the minimum number of outcomes that completes the sentence.
An image in a quiz
Correct Answer:The first stage of the trial has...,a minimum of four outcomes.

a minimum of four outcomes.

Correct Answer:The second stage of the trial has...,a minimum of three outcomes.

a minimum of three outcomes.

Correct Answer:The third stage of the trial has...,a minimum of two outcomes.

a minimum of two outcomes.

Correct Answer:The whole trial has...,a minimum of 24 outcomes.

a minimum of 24 outcomes.

Q5.
This Venn diagram and outcome tree both show events for the same trial. Match each letter in the outcome tree to the correct outcome from the Venn diagram.
An image in a quiz
Correct Answer:a,18

18

Correct Answer:b,90

90

Correct Answer:c,27

27

Correct Answer:d,no outcome

no outcome

Correct Answer:e,773

773

Q6.
This Venn diagram and outcome tree both show events for the same trial. Match each letter in the Venn diagram to the correct outcome from the outcome tree.
An image in a quiz
Correct Answer:a,45

45

Correct Answer:b,55

55

Correct Answer:c,15

15

Correct Answer:d,120

120

Correct Answer:e,196

196