Tree diagrams are a representation used to model statistical/probability questions. Branches represent different possible events or outcomes.

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.

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

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

Maths

In this unit, pupils learn techniques for systematically listing all of the possible outcomes for both one event and two events. In the future unit, pupils use lists of outcomes to find theoretical probabilities

In this unit, pupils find all the factors of a number systematically and they understand that systematic listing is helpful in organising their work. The idea of being systematic is built on in this unit as pupils work to identify all possible outcomes

Probability: possible outcomes

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?

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: 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?

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.

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 {{ }}.

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

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

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

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.

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 {{ }}.

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.

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

Starter Quiz