What is important to know about Tree diagrams?

Multiply along branches to get the probability of combined outcomes.

Add probabilities for mutually exclusive outcomes.

All probabilities on branches from one point must add up to 1.

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Statistics & Probability · Foundation & Higher

Tree diagrams

Tree diagrams show all possible outcomes of two or more events and their probabilities. You multiply along branches and add between branches.

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1Multiply along branches to get the probability of combined outcomes.
2Add probabilities for mutually exclusive outcomes.
3All probabilities on branches from one point must add up to 1.
4For "without replacement", the probabilities on the second set of branches change.

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Example 1

A bag has 4 red and 6 blue balls. A ball is drawn, replaced, then another is drawn. Find P(both red).

Working

AnswerP(both red) = 4/25

⚠️

✗Adding instead of multiplying along branches.

✗Forgetting to update probabilities for "without replacement" questions.

✗Not checking that branches at each node sum to 1.

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✓Draw the tree clearly with all outcomes and probabilities labelled on each branch.

✓Circle or highlight the branches you need before multiplying.

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