New
New
Year 9

Using an outcome tree to display outcomes for two events

I can systematically find all the possible outcomes for two events by using an outcome tree diagram.

New
New
Year 9

Using an outcome tree to display outcomes for two events

I can systematically find all the possible outcomes for two events by using an outcome tree diagram.

Lesson details

Key learning points

  1. Possible outcomes for two events can be shown in an outcome tree diagram.
  2. The outcome tree diagram can be used to generate either an outcome table or list.
  3. An outcome tree can be generated from either an outcome table or list.

Common misconception

Every group of branches should have the same number of branches.

In a multi-staged trial, each stage may have a different number of outcomes. The number of branches in each group reflects the number of outcomes of a stage. This means each group of branches can be made from a different number of branches.

Keywords

  • Tree diagrams - 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.

  • Sample space - A sample space is all the possible outcomes of a trial. A sample space diagram is a systematic way of producing a sample space.

This lesson will focus on outcome trees, which demonstrate one particular purpose of a tree diagram. These outcome trees will focus on an understanding of how to show outcomes of a 1-stage or 2-stage trial on an outcome tree. There will be no probabilities attached to the branches this lesson.
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.
Which of these are equivalent to $$1\over5$$?
Correct answer: $$2\over10$$
$$6\over10$$
$$0.5$$
Correct answer: $$0.2$$
Correct answer: $$20$$%
Q2.
Andeep carries out the following trial: spinning this spinner once. Which of these is the sample space of distinct outcomes for Andeep's trial?
An image in a quiz
There are 5 sectors.
There are 4 distinct outcomes.
{A, A, B, C, D}
Correct answer: {A, B, C, D}
{A, A} is the repeated outcome.
Q3.
Each sector in a spinner is of equal size. In which spinners are the outcomes of “win” and “lose” equally likely?
An image in a quiz
A
Correct answer: B
Correct answer: C
D
Q4.
A fair, 6-sided dice has outcomes: {2, 3, 4, 5, 6, 7}. Which of these events is most likely to happen?
multiple of 2
multiple of 3
even number
Correct answer: prime number
square number
Q5.
A fair 6-sided dice has outcomes: {1, 2, 3, 4, 5, 6}. Event: if the dice lands on a prime number, Aisha wins. Which of these outcome spinners most closely represents the likelihood of Aisha winning?
An image in a quiz
A
B
Correct answer: C
D
E
Q6.
Trial: a spinner will be spun twice. The outcome of each spin will be multiplied together. The spinner has outcomes: {2, 5, 7, 11, 15}. Match the letters to their correct value in the outcome table.
An image in a quiz
Correct Answer:A,30

30

Correct Answer:B,11

11

Correct Answer:C,121

121

Correct Answer:D,10

10

Correct Answer:E,5

5

6 Questions

Q1.
The outcome tree represents all outcomes from spinning the spinner once. Which outcomes are missing from the outcome tree?
An image in a quiz
3
6
Correct answer: 9
12
Correct answer: 14
Q2.
The outcome tree represents all outcomes from spinning spinner P and spinner Q once each. Match each letter to its value.
An image in a quiz
Correct Answer:a,16

16

Correct Answer:b,27

27

Correct Answer:c,8

8

Q3.
This outcome tree represents all outcomes from spinning spinner R twice. The sample space shows the outcomes when the results of each spin are added. Match each letter to its value.
An image in a quiz
Correct Answer:a,11

11

Correct Answer:b,16

16

Correct Answer:c,13

13

Q4.
Trial: spinning this spinner once. Event: the spinner landing on a prime number. Which group of outcomes should be written inside the box?
An image in a quiz
2, 3, 4, 5, 7
2, 3, 5, 7, 11
3, 5, 7, 11
Correct answer: 4, 6, 9
2, 4, 6, 9
Q5.
This incomplete outcome tree represents all outcomes from spinning spinner X twice and adding the results of each spin. In the sample space, match the letter to its value.
An image in a quiz
Correct Answer:a,6

6

Correct Answer:b,14

14

Correct Answer:c,15

15

Correct Answer:d,5

5

Correct Answer:e,10

10

Q6.
Trial: spinning this spinner once. Event 1: the spinner landing on a even number. Event 2: the spinner landing on a square number. Which of these outcomes should be written inside the box?
An image in a quiz
2
9
Correct answer: 21
25
Correct answer: 31