Likelihood describes the chance that a particular event will occur.

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

Equally likely outcomes

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

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

An event is a subset of a sample space. It could be a particular outcome or be a set of outcomes that may occur from a trial.

Non-equally likely outcomes

An outcome is impossible if there is no possibility that it can happen.

An outcome is certain if it is guaranteed to happen.

An outcome has even chance if its likelihood of happening is the same as its likelihood of not happening.

The scale of likelihoods

An experiment is a repetition of a trial multiple times in order to observe how often each outcome occurs.

Experiments to determine how likely an outcome is

When listing outcomes systematically, they are listed in such a way as to ensure all outcomes are recorded.

Using lists to display outcomes for two events

An outcome table is a table that shows all the possible outcomes.

Using two-way tables to display outcomes for two events

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.

Using an outcome tree to display outcomes for two events

Venn diagrams are a representation used to model statistical/probability questions. Commonly circles are used to represent events.

Using a Venn diagram to display outcomes for two events

Venn diagrams are a representation used to diagram statistical/probability questions. Commonly circles are used to represent events.

Probability: possible outcomes

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