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 two events

Maths

Equally likely outcomes

Non-equally likely outcomes

The scale of likelihoods

Experiments to determine how likely an outcome is

Using lists to display outcomes for two events

Using two-way tables to display outcomes for two events

Using a Venn diagram to display outcomes for two events

Comparing representations of outcomes for two events

Using lists to display outcomes for more than two events

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

Using a Venn diagram to display outcomes for more than two events

Comparing representations of outcomes for more than two events

Problem solving with possible outcomes

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

This unit introduces and explores the concept of liklihood as a relative measure, and demonstrates multiple ways to represent likelihood such as Venn diagrams, tree diagrams and two-way tables.

Probability: possible outcomes

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

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

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.

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


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.

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?

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

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

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

A fair, 6-sided dice has outcomes: {2, 3, 4, 5, 6, 7}. 
Which of these events is most likely to happen?

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?

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.

Starter Quiz

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