IGCSE Tree Diagrams: Complete Guide for Cambridge IGCSE Mathematics

IGCSE tree diagrams are essential probability topics in Cambridge IGCSE Mathematics that appear in both Paper 2 and Paper 4. Mastering drawing tree diagrams, multiplying along branches, and finding probabilities is essential for solving complex probability problems.

This comprehensive IGCSE tree diagrams guide covers everything you need to know, including drawing tree diagrams, calculating probabilities from trees, worked examples, common exam questions, and expert tips from Tutopiya’s IGCSE maths tutors. We’ll also show you how to avoid the most common mistakes that cost students valuable marks.

🎯 What you’ll learn: By the end of this guide, you’ll know how to draw tree diagrams, multiply probabilities along branches, find combined probabilities, and apply these skills to solve problems in IGCSE exams.

Already studying with Tutopiya? Practice these skills with our dedicated IGCSE Statistics practice deck featuring exam-style questions and instant feedback.

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Why IGCSE Tree Diagrams Matter

IGCSE tree diagrams are essential probability topics. Here’s why they’re so important:

• High frequency topic: Tree diagram questions appear regularly in IGCSE maths papers
• Foundation skill: Essential for visualizing and solving probability problems
• Exam weight: Typically worth 5-8 marks per paper
• Real-world applications: Used in decision-making and probability analysis
• Problem-solving skills: Develops systematic approach to probability problems

Key insight from examiners: Students often forget to multiply along branches or make errors with dependent events. This guide will help you master these systematically.

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Understanding Tree Diagrams

Tree diagrams show all possible outcomes of probability experiments with branches representing choices.

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Drawing Tree Diagrams

Steps:

1. Start with initial event
2. Draw branches for each possible outcome
3. Write probabilities on branches
4. Continue for subsequent events
5. Multiply along branches to find path probabilities

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Example 1: Simple Tree Diagram

A coin is flipped twice. Draw tree diagram.

Solution:

        H (0.5)
       /
Start
       \
        T (0.5)

Then from each, branch to H and T again.

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Multiplying Along Branches

Rule: Multiply probabilities along the path to find probability of that outcome.

Example 2: Probability of heads = 0.5. Flip twice. Find P(both heads).

Solution: P(H, H) = 0.5 × 0.5 = 0.25

Answer: 0.25

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Dependent Events in Tree Diagrams

Example 3: Bag has 5 red, 3 blue. Pick two without replacement. Draw tree diagram.

Solution: First pick: P(red) = 5/8, P(blue) = 3/8 If first red: P(second red) = 4/7, P(second blue) = 3/7 If first blue: P(second red) = 5/7, P(second blue) = 2/7

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Finding Combined Probabilities

Example 4: Using tree diagram, find P(one red, one blue) in any order.

Solution: P(red then blue) = 5/8 × 3/7 = 15/56 P(blue then red) = 3/8 × 5/7 = 15/56 P(one red, one blue) = 15/56 + 15/56 = 30/56 = 15/28

Answer: 15/28

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Common Examiner Traps

• Forgetting to multiply - Always multiply probabilities along branches
• Dependent event errors - Adjust probabilities for second event
• Adding vs multiplying - Multiply along path, add for “or” outcomes

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Practice Questions

Question 1

Probability of rain = 0.3. If rains, probability of event cancelled = 0.8. Draw tree diagram and find P(event cancelled).

Solution: P(rain and cancelled) = 0.3 × 0.8 = 0.24 P(no rain and cancelled) = 0.7 × 0 = 0 P(cancelled) = 0.24 + 0 = 0.24

Answer: 0.24

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Frequently Asked Questions About IGCSE Tree Diagrams

What is a tree diagram?

A tree diagram shows all possible outcomes of probability experiments with branches representing choices.

How do I find probabilities from tree diagrams?

Multiply probabilities along the path to find probability of that specific outcome.

How do I handle dependent events in tree diagrams?

Adjust probabilities for the second event based on what happened in the first event.

When should I add probabilities?

Add probabilities when finding “or” outcomes (e.g., P(A or B)).

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Related IGCSE Maths Resources

Strengthen your IGCSE Mathematics preparation with these comprehensive guides:

• IGCSE Probability Applications: Complete Guide - Master probability
• IGCSE Venn Diagrams: Complete Guide - Master Venn diagrams
• IGCSE Maths Revision Notes, Syllabus and Preparation Tips - Complete syllabus overview, topic breakdown, and revision strategies
• IGCSE Past Papers Guide - Access free IGCSE past papers and exam resources

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Next Steps: Master IGCSE Tree Diagrams with Tutopiya

Ready to excel in IGCSE tree diagrams? Our expert IGCSE maths tutors provide:

• Personalized 1-on-1 tutoring tailored to your learning pace
• Exam-focused practice with real Cambridge IGCSE past papers
• Interactive whiteboard sessions for visual learning
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• Flexible scheduling to fit your revision timetable

Book a free IGCSE maths trial lesson and get personalized support to master tree diagrams and achieve your target grade.

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