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

1. First set of branches – e.g. first pick (probabilities on branches).
2. Second set of branches – from each first branch, same structure for second stage (conditional probabilities if “without replacement”).
3. Multiply along each path to get probability of that outcome.
4. 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.