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Tree Diagrams

(KS3, Year 7)

A tree diagram shows all the possible outcomes of an event and their probabilities.

A Real Example of a Tree Diagram

It is easier to understand a tree diagram with an example.

Tossing a Coin

If a coin is tossed, the coin can land on Heads or Tails. coin_toss_tree

Each outcome has its own branch. There is a branch for Heads and for Tails.
The probability of each outcome is written by each branch. The probability of Heads (¹⁄₂) is written by the branch. The probability of Tails (¹⁄₂) is written by the branch.

Note: The probabilities across the branches add up to 1. They are mutually exclusive and exhaustive events.

Another Real Example of a Tree Diagram

A tree diagram can be extended to more than one event. The tree diagram below is for two coin tosses. coin_toss_twice_tree

What Is Probability?

A probability is a measure of how likely (how probable) an event is to happen. A probability is expressed as a number between 0 (impossible) and 1 (certain). The formula for finding a probability is shown below: probability_formula_mini