Probability

Topic overview

What you need to know

Probability is a key part of GCSE Mathematics. Build fluency with the method, then apply it to unfamiliar and multi-step problems. A measure of how likely an event is to occur, ranging from 0 (impossible) to 1 (certain). P(event) = favourable outcomes ÷ total outcomes. The set of all possible outcomes of an experiment. E.g. for a die: {1, 2, 3, 4, 5, 6}. Events that cannot happen at the same time. P(A or B) = P(A) + P(B).

Exam tip

Write every stage of your method. Method marks can still be earned when the final answer is wrong.

Revision notes

Core ideas

Secure these ideas first. Say each definition in your own words, then connect it to the topic overview.

Probability: A measure of how likely an event is to occur, ranging from 0 (impossible) to 1 (certain). P(event) = favourable outcomes ÷ total outcomes.
Sample Space: The set of all possible outcomes of an experiment. E.g. for a die: {1, 2, 3, 4, 5, 6}.
Mutually Exclusive Events: Events that cannot happen at the same time. P(A or B) = P(A) + P(B).
Independent Events: Events where the outcome of one does not affect the other. P(A and B) = P(A) × P(B).

Revision notes

Apply it in the exam

The exam will rarely ask for an isolated definition. Practise selecting the right idea and using it as part of a complete explanation or method.

Tree Diagram: A branching diagram showing all possible outcomes and their probabilities. Multiply along branches, add between branches.
Relative Frequency: An estimate of probability based on experiments: relative frequency = number of successes ÷ number of trials.
Complementary Events: P(not A) = 1 − P(A). The probability of an event NOT happening.
Conditional Probability: The probability of an event given that another event has already occurred. Shown on tree diagrams with changed probabilities on second branches.

Core knowledge

Key facts for Probability

8 essentials

A measure of how likely an event is to occur, ranging from 0 (impossible) to 1 (certain). P(event) = favourable outcomes ÷ total outcomes.

Sample Space

The set of all possible outcomes of an experiment. E.g. for a die: {1, 2, 3, 4, 5, 6}.

Mutually Exclusive Events

Events that cannot happen at the same time. P(A or B) = P(A) + P(B).

Independent Events

Events where the outcome of one does not affect the other. P(A and B) = P(A) × P(B).

Tree Diagram

A branching diagram showing all possible outcomes and their probabilities. Multiply along branches, add between branches.

Relative Frequency

An estimate of probability based on experiments: relative frequency = number of successes ÷ number of trials.

Complementary Events

P(not A) = 1 − P(A). The probability of an event NOT happening.

Conditional Probability

The probability of an event given that another event has already occurred. Shown on tree diagrams with changed probabilities on second branches.

Active recall

Close the notes and answer these

1.Without looking, explain probability and give one example or consequence.
2.Without looking, explain sample space and give one example or consequence.
3.Without looking, explain mutually exclusive events and give one example or consequence.
4.Without looking, explain independent events and give one example or consequence.

Content reviewed 23 July 2026 against the current linked specification.

Finished learning?

Mark the notes complete, then test what you can recall.

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