New
New
Year 9

Problem solving with possible outcomes

I can choose an appropriate diagram to display the outcomes for different events.

New
New
Year 9

Problem solving with possible outcomes

I can choose an appropriate diagram to display the outcomes for different events.

Lesson details

Key learning points

  1. The possible outcomes can be displayed for two or more events using an appropriate diagram.
  2. The various diagrams can be evaluated and the appropriateness of each diagram decided.
  3. The likelihood of an outcome can be determined using a mixture of different diagrams.

Common misconception

Outcome tables and outcome trees only work for outcomes that are all equally likely.

Outcome tables can be separated into more rows and columns, and outcome trees split into more branches, to show outcomes that are more or less likely than other ones. This does mean these diagrams do get massive very quickly!

Keywords

  • Likelihood - Likelihood describes the chance that a particular event occurs.

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

This lesson aims to serve as a subtle demonstration of how probability can be a way of making increasingly massive outcome trees and outcome tables more efficient when attempting to show the different likelihoods of unequally likely outcomes to multi-stage events.
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).

Loading...

6 Questions

Q1.
The Venn diagram shows the sample space $$\xi$$ = {8, 81, 144, 201}. Match each region to the correct outcome.
An image in a quiz
Correct Answer:a,8

8

Correct Answer:b,144

144

Correct Answer:c,81

81

Correct Answer:d,201

201

Q2.
The Venn diagram shows a selection of subjects that Andeep and Sam enjoy. Which of these statements is true for science?
An image in a quiz
Andeep likes science, but Sam does not like science.
Both Andeep and Sam like science.
Andeep does not like science, but Sam likes science.
Correct answer: Neither Andeep nor Sam like science.
Q3.
Both the Venn diagram and outcome table represent the same two events from a trial. Match each lettered outcome from the outcome table to the correct outcome from the Venn diagram.
An image in a quiz
Correct Answer:a,28

28

Correct Answer:b,35

35

Correct Answer:c,280

280

Correct Answer:d,77

77

Q4.
Trial: spinning this spinner once. Event 1: even number. Event 2: cube number. Which outcomes should be written inside the box?
An image in a quiz
0
Correct answer: 1
8
11
Correct answer: 27
Q5.
Trial: a spinner is spun twice, with the two results multiplied together. Both incomplete diagrams represent the same trial. Match each letters to the correct outcome.
An image in a quiz
Correct Answer:a,21

21

Correct Answer:b,5

5

Correct Answer:c,49

49

Correct Answer:d,7

7

Correct Answer:e,15

15

Q6.
Trial: Spinner 1 is spun twice. The outcome of each spin is added together. This incomplete outcome tree shows all outcomes of this trial. Match each letter to its value in the sample space.
An image in a quiz
Correct Answer:a,56

56

Correct Answer:b,14

14

Correct Answer:c,84

84

Correct Answer:d,21

21

6 Questions

Q1.
Trial: The spinner is spun twice. The order of the two outcomes doesn't matter. The incomplete outcome table shows all outcomes of the trial. Match each letter the sample space to its value.
An image in a quiz
Correct Answer:a,X X

X X

Correct Answer:b,Y X

Y X

Correct Answer:c,Y Y

Y Y

Correct Answer:d,Z X

Z X

Correct Answer:e,Z Z

Z Z

Q2.
Trial: The spinner is spun twice. The order of the two outcomes doesn't matter. Which of these statements are correct for this trial?
An image in a quiz
Correct answer: One outcome is more likely to happen than any other outcome.
Two equally likely outcomes are both the most likely to happen.
Two equally likely outcomes are both the least likely to happen.
The most likely outcome is three times as likely as the least likely outcome.
Correct answer: The most likely outcome is nine times as likely as the least likely outcome.
Q3.
Trial: The product of two spins of the spinner. This outcome table represents all outcomes of the trial. Match the start of each statement to the correct end of the statement.
An image in a quiz
Correct Answer:The event that Alex wins...,is the most likely outcome.

is the most likely outcome.

Correct Answer:The event that Sam wins...,is in between the least and most likely outcomes on a likelihood scale

is in between the least and most likely outcomes on a likelihood scale

Correct Answer:The event that they draw...,is the least likely outcome.

is the least likely outcome.

Q4.
Trial: The spinner will be spun once. Which of these statements about one stage of this trial is correct?
An image in a quiz
The spinner is twice as likely to land on X compared to Y.
The spinner is twice as likely to land on Y compared to X.
Correct answer: The spinner is three times as likely to land on Y compared to X.
It is possible to split this spinner into 6 equally likely outcomes.
Correct answer: It is possible to split this spinner into 8 equally likely outcomes.
Q5.
Trial: The spinner will be spun twice, and the order of the two stages does not matter. Match the start of each statement to the correct outcome.
An image in a quiz
Correct Answer:The most common outcome is...,Y Y

Y Y

Correct Answer:The least common outcome is...,X X

X X

Correct Answer:Y Y appears 1.5× as often as...,XY

XY

Q6.
Trial: Spinner A and B are spun once each. The sum of the two outcomes is found. Which of these statements about the outcomes of this trial are correct?
An image in a quiz
Correct answer: 12 is the most likely outcome.
-13 is the most likely outcome.
The most likely outcome is 4 times as likely than the least likely outcome.
Correct answer: The most likely outcome is 8 times as likely than the least likely outcome.
Correct answer: The most likely outcome is twice as likely than the second most likely outcome.