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MathidiaMathematics Academy
Conditional and combined probability
Lesson 66 of 75
Introduction

Tree diagrams

Objective. Calculate probabilities along and across branches.

  1. 1. Learn
  2. 2. Worked example
  3. 3. Practice
  4. 4. Feedback
  5. 5. Continue

Learn: the key idea

Tree diagrams show the probabilities of combined events across successive branches, where you multiply along a branch and add across separate branches. Each set of branches from a point must sum to 1, and multiplying along a path gives the probability of that specific sequence of outcomes. For example, if P(rain) = 0.3 and P(late | rain) = 0.4, then P(rain and late) = 0.3 × 0.4 = 0.12. To find the probability of an outcome happening in more than one way, add the probabilities of each relevant path together.

Worked example

A tree diagram shows P(win first game) = 0.6 and P(win second game | win first) = 0.5. Find the probability of winning both games.

0.6 … 0.5
Illustrated card showing 0.6 … 0.5
  1. 1Identify the two branches: win first then win second
  2. 2Multiply along the branches: 0.6 × 0.5
  3. 30.6 × 0.5 = 0.3
  4. 4Probability of winning both games = 0.3

Answer: 0.3

Concept mastery

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Practice

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Common mistake. Students often add probabilities along a single branch instead of multiplying; remember to multiply along branches for a combined event and only add across separate complete paths.

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