New
New
Year 9

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

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

New
New
Year 9

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

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

warning

These resources will be removed by end of Summer Term 2025.

Switch to our new teaching resources now - designed by teachers and leading subject experts, and tested in classrooms.

Lesson details

Key learning points

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

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.

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!

As the outcome trees become more complex, it is important to encourage students to keep to their systematic processes, such as writing down the outputs on the branches in a sensible order, such as alphabetically or numerically.
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).

Lesson video

Loading...

6 Questions

Q1.
Trial: The coin and spinner are both spun once each. Which of these statements are true?
An image in a quiz
Correct answer: 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.
Correct answer: There are 24 outcomes from this trial.
Q2.
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.
An image in a quiz
Correct Answer: 15, 15 outcomes, 15 branches
Q3.
Trial: flipping the coin and spinning the spinner once each. Which of these are representations that show the complete sample space of this trial?
An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
Correct Answer: An image in a quiz
An image in a quiz
An image in a quiz
Q4.
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 .
An image in a quiz
Correct Answer: 5, 5 outcomes
Q5.
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.
An image in a quiz
Correct Answer:a,1

1

Correct Answer:b,9

9

Correct Answer:c,36

36

Correct Answer:d,4

4

Correct Answer:e,16

16

Q6.
Trial: spinning this spinner once. Event 1: even number. Event 2: square number. The outcome that should be written inside the box is .
An image in a quiz
Correct Answer: 10, ten

6 Questions

Q1.
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?
An image in a quiz
1
Correct answer: 2
Correct answer: 7
9
Q2.
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?
An image in a quiz
Spinner X lands on 7 and spinner Y lands on 9.
Spinner Y lands on 7 and spinner X lands on 9.
Correct answer: Spinner X lands on 7, and then lands on 2. Spinner Y lands on 9.
Correct answer: 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.
Q3.
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.
Correct Answer: 8, 8 outcomes
Q4.
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 .
An image in a quiz
Correct Answer: 28
Q5.
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
An image in a quiz
Correct Answer:a,E

E

Correct Answer:b,G

G

Correct Answer:c,TGH

TGH

Correct Answer:d,G

G

Correct Answer:e,UGI

UGI

Q6.
Trial: spinning this spinner once. Event 1: even number. Event 2: square number. Event 3: prime number. Match each letter to its outcome.
An image in a quiz
Correct Answer:a,not possible

not possible

Correct Answer:b,2

2

Correct Answer:c,18

18

Correct Answer:d,9

9

Correct Answer:e,15

15