Tree Diagrams

This lesson covers how to draw and use tree diagrams, applying the AND and OR rules, and calculating combined probabilities for independent events and dependent events (without replacement). Tree diagrams are one of the most important probability tools on the Edexcel GCSE Mathematics (1MA1) exam, appearing on both Foundation and Higher tier papers.

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What Is a Tree Diagram?

A tree diagram shows all possible outcomes of two or more successive events. Each "branch" represents a possible outcome, and the probability is written on the branch.

Key Rules

Rule	When to use	How to calculate
AND rule (multiplication)	Both events happen in sequence	Multiply along the branches
OR rule (addition)	Either one outcome or another	Add the final probabilities

Important Properties

• The probabilities on each set of branches from the same point must add up to 1.
• To find the probability of a particular path, multiply along that path.
• To find the probability of one outcome or another, add the relevant path probabilities.

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Independent Events — With Replacement