Using an outcome tree to display outcomes for two events | Maths

Starter quiz

Which of these are equivalent to $1\over5$ ?

$2\over10$ ✓

$6\over10$

$0.5$

$0.2$ ✓

$20$ % ✓
Andeep carries out the following trial: spinning this spinner once. Which of these is the sample space of distinct outcomes for Andeep's trial?

There are 5 sectors.

There are 4 distinct outcomes.

{A, A, B, C, D}

{A, B, C, D} ✓

{A, A} is the repeated outcome.
Each sector in a spinner is of equal size. In which spinners are the outcomes of “win” and “lose” equally likely?

A

B ✓

C ✓

D
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

prime number ✓

square number
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?

A

B

C ✓

D

E
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.

A

⇔

30 ✓

B

⇔

11 ✓

C

⇔

121 ✓

D

⇔

10 ✓

E

⇔

5 ✓

Exit quiz

The outcome tree represents all outcomes from spinning the spinner once. Which outcomes are missing from the outcome tree?

3

6

9 ✓

12

14 ✓
The outcome tree represents all outcomes from spinning spinner P and spinner Q once each. Match each letter to its value.

a

⇔

16 ✓

b

⇔

27 ✓

c

⇔

8 ✓
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.

a

⇔

11 ✓

b

⇔

16 ✓

c

⇔

13 ✓
Trial: spinning this spinner once. Event: the spinner landing on a prime number. Which group of outcomes should be written inside the box?

2, 3, 4, 5, 7

2, 3, 5, 7, 11

3, 5, 7, 11

4, 6, 9 ✓

2, 4, 6, 9
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.

a

⇔

6 ✓

b

⇔

14 ✓

c

⇔

15 ✓

d

⇔

5 ✓

e

⇔

10 ✓
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?

2

9

21 ✓

25

31 ✓

Worksheet

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Video

Lesson Details

Key learning points

Possible outcomes for two events can be shown in an outcome tree diagram.
The outcome tree diagram can be used to generate either an outcome table or list.
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.