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

Starter quiz

Trial: The coin and spinner are both spun once each. Which of these statements are true?

There are 2 stages to this trial. ✓

There are 14 stages to this trial.

There are 2 outcomes from this trial.

There are 14 outcomes from this trial.

There are 24 outcomes from this trial. ✓
Trial: Spinner R and spinner T will both be spun once. The outcomes of this trial are represented on this outcome tree. In total there will there be ______ branches in layer 2 of the outcome tree.

'15' ✓
Trial: flipping the coin and spinning the spinner once each. Which of these are representations that show the complete sample space of this trial?
Trial: spinning this spinner once. Event: factor of 84. This event and its opposite event are represented on an outcome tree. The number of outcomes that should be written inside the box is ______.

'5' ✓
This incomplete outcome tree represents all outcomes from spinning spinner X twice and multiplying the results of each spin. Match each letter in the sample space to its value.

a

⇔

1 ✓

b

⇔

9 ✓

c

⇔

36 ✓

d

⇔

4 ✓

e

⇔

16 ✓
Trial: spinning this spinner once. Event 1: even number. Event 2: square number. The outcome that should be written inside the box is ______.

'10' ✓

Exit quiz

Trial: spinning spinner X twice and spinning spinner Y once. The incomplete outcome tree shows this trial. Which outcomes could go in place of the letter a?

1

2 ✓

7 ✓

9
Trial: spinning spinner X twice and spinning spinner Y once. Which of these statements could be true for the highlighted set of branches on this incomplete outcome tree?

Spinner X lands on 7 and spinner Y lands on 9.

Spinner Y lands on 7 and spinner X lands on 9.

Spinner X lands on 7, and then lands on 2. Spinner Y lands on 9. ✓

Spinner X lands on 7, and then lands on 7. Spinner Y lands on 9. ✓

Spinner X lands on 7. Spinner Y lands on 9, and then lands on 9.
Trial: a coin {heads, tails} is flipped three times. The number of outcomes there are in this trial is ______. Sketch an outcome tree to help you.

'8' ✓
Trial: Spinner A is spun twice and coin flipped. The outcome of each spin is added together. This incomplete outcome tree shows all the trial's outcomes. The value of a in the sample space is ______.

'28' ✓
Trial: spinners 1, 2, and 3 will be spun once each. This incomplete outcome tree represents all outcomes of this trial. Match a, b, c, d, and e to the correct outcome of the trial or stage

a

⇔

E ✓

b

⇔

G ✓

c

⇔

TGH ✓

d

⇔

G ✓

e

⇔

UGI ✓
Trial: spinning this spinner once. Event 1: even number. Event 2: square number. Event 3: prime number. Match each letter to its outcome.

a

⇔

not possible ✓

b

⇔

2 ✓

c

⇔

18 ✓

d

⇔

9 ✓

e

⇔

15 ✓

Worksheet

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Video

Lesson Details

Key learning points

Possible outcomes for more than two events can be shown in an outcome tree diagram.
The outcome tree diagram can be used to generate a list.
An outcome tree can be generated from a list.

Common misconception

An outcome tree can only have a maximum of three layers of branches.

An outcome tree can have as many layers of branches as needed, depending on the number of stages there are in a trial. For example, if a trial involved flipping 7 coins, then there would be 7 layers of branches! That's too probably too many to draw!

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.