Probability Trees IGCSE: How to Draw Them and Score Full Marks
Probability trees are one of the most searched IGCSE maths topics because they appear in statistics/probability questions and many students lose marks on structure or calculation. Used correctly, they make multi-step probability questions clear and easy to mark.
When to Use a Probability Tree
- Two or more stages (e.g. picking two balls, or doing something then doing it again).
- Sequential events where each branch has a probability and you want “and” (multiply) or “or” (add) outcomes.
Draw one branch per outcome at each stage; label each branch with the probability; outcomes are multiply along the branch; add the probabilities of the outcomes that match the question.
How to Draw and Use the Tree
- First set of branches – e.g. first pick (probabilities on branches).
- Second set of branches – from each first branch, same structure for second stage (conditional probabilities if “without replacement”).
- Multiply along each path to get probability of that outcome.
- Add the paths that match the event you want (e.g. “both red”, “one of each”).
Check: probabilities from one node should add to 1; all outcome probabilities should add to 1 (for a complete set).
Worked Example and Where Probability Trees Appear
Example: A bag has 3 red and 2 blue balls. Two balls are drawn without replacement. Find P(both red). First branch: P(red) = 3/5. Second branch (from red): P(red) = 2/4. So P(both red) = (3/5) × (2/4) = 6/20 = 3/10. For “without replacement” the probabilities on the second set of branches change. Common errors: Forgetting to multiply along branches (and add between outcomes); wrong conditional probabilities when not replacing; not checking that probabilities from one node add to 1. Probability trees appear in statistics questions and real-life contexts (e.g. sports, quality control).
Tutopiya Resources and Free Trial
Tutopiya’s IGCSE Maths tutors can help you master probability trees and combine them with two-way tables or listing outcomes where needed.
Book a free trial with an IGCSE Maths tutor or explore Tutopiya’s learning portal for free resources and probability practice.
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