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Year 9

Comparing representations of outcomes for two events

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

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New
New
Year 9

Comparing representations of outcomes for two events

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

Download all resources
Share activities with pupils

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

An outcome tree doesn't have a sample space.

Each representation of the outcomes of a trial have a sample space as a part of it. For an outcome table, the table itself is the sample space. For an outcome tree, a sample space must always be constructed after drawing the two layers of branches.

Keywords

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

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

There is no "rule" for when a list, outcome table, or outcome tree becomes better than the other representations - often this comes down to personal preference. However, there are times when one representation is clearly unsuitable, such as constructing an outcome tree made of 36 branches.
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).

Video

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Starter quiz

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6 Questions

Q1.
The number of outcomes on this spinner that are odd numbers is .
An image in a quiz
Correct Answer: 4, 4 outcomes
Q2.
Trial: flipping the coin and spinning the spinner once each. Which of these lists of outcomes for the trial show a complete sample space? Use H for 'heads' and T for 'tails'.
An image in a quiz
{H, T, A, B, C}
{H, T, A, B, C, A, B, C}
Correct answer: {HA, HB, HC, TA, TB, TC}
{HT, AB, AB, CB}
Correct answer: {TB, HA, TC, HC, TA, HB}
Q3.
Trial: spinning this spinner once. Event: multiple of 3. Which of these outcomes should be written inside the box?
An image in a quiz
Correct answer: 2
3
6
Correct answer: 8
24
Q4.
Match each number to its correct location on the Venn diagram.
An image in a quiz
Correct Answer:5,a

a

Correct Answer:9,b

b

Correct Answer:4,c

c

Correct Answer:6,d

d

Q5.
The Venn diagram shows a selection of types of TV shows that Jacob and Izzy do and do not like. Which of these statements is true for drama TV shows?
An image in a quiz
Both Jacob and Izzy like drama shows.
Correct answer: Jacob likes drama shows, but Izzy doesn't.
Izzy likes drama shows, but Jacob doesn't.
Neither Jacob nor Izzy like drama shows.
Q6.
This incomplete outcome tree represents all outcomes from spinning spinner R twice and adding the results of each spin. Match each letter to its value in the sample space.
An image in a quiz
Correct Answer:a,10

10

Correct Answer:b,12

12

Correct Answer:c,15

15

Correct Answer:d,7

7

Correct Answer:e,14

14

Exit quiz

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6 Questions

Q1.
Which of these are helpful when trying to systematically write down all outcomes for a two-stage trial?
Correct answer: list
Correct answer: outcome table
Correct answer: outcome tree
Venn diagram
Q2.
Both the outcome table and outcome tree represent the same two-stage trial. Which outcomes go in the two locations marked by a question mark?
An image in a quiz
Correct answer: A
Correct answer: B
1
2
5
Q3.
Which statements are correct for this outcome table and outcome tree?
An image in a quiz
Correct answer: A and B are the only two outcomes for one stage of this trial.
The event looks at only odd numbers.
Correct answer: The first layer of branches represent only two outcomes.
Correct answer: Each group in the second layer of branches represent three outcomes.
All the outcomes can be placed on the outcome tree in any order.
Q4.
Both the Venn diagram and outcome tree represent the same two events from a trial. Match each missing outcome from the outcome tree to an outcome from the Venn diagram
An image in a quiz
Correct Answer:a,10

10

Correct Answer:b,466

466

Correct Answer:c,3

3

Correct Answer:d,1893

1893

Q5.
Both the outcome tree and Venn diagram represent the same two events from a trial. Match the missing outcome from the Venn diagram to an outcome from the outcome tree.
An image in a quiz
Correct Answer:a,1

1

Correct Answer:b,210

210

Correct Answer:c,15

15

Correct Answer:d,93

93

Q6.
Trial: Alex will spin this spinner and flip this coin, and then write the product of the two outcomes in the sample space. Which of these are the missing numbers on the spinner?
An image in a quiz
Correct answer: 0
1
Correct answer: 2
Correct answer: 5
Correct answer: 11