Probability Trees
Tree diagrams organise multi-stage probability problems into a clear visual structure. Students multiply along branches for combined probabilities and add between branches for alternative outcomes.
What You'll Learn
- Drawing tree diagrams for two or more successive events
- Multiplying along branches to find combined probabilities
- Adding probabilities of different outcomes (OR scenarios)
- Handling dependent events where probabilities change (without replacement)
Watch Out For These Mistakes
Students make these errors again and again. Knowing them in advance gives you a head start.
Adding probabilities along a branch instead of multiplying
Forgetting to adjust probabilities for the second event in without-replacement problems
Not including all relevant branches when answering the question
What Examiners Say About Probability Trees
Insights pulled from Cambridge IGCSE (0580) examiner reports — the exact mistakes candidates make every year.
- Common Mistake●●●●●
In probability without replacement, the denominator DECREASES by 1 for each subsequent pick (13 → 12 → 11...). Getting 104/169 instead of the correct answer usually means you forgot this.
Source: CIE 0580 · Feb/March 2024 · Paper 2 · Q25
- Common Mistake●●●●●
For 'exactly one green button' out of two picks, there are TWO orderings: green-then-not OR not-then-green. Calculate one product and DOUBLE it (or add both products).
Source: CIE 0580 · May/June 2023 · Paper 4 · Q15
- Technique●●●●●
In a histogram, bar HEIGHT = frequency density (frequency ÷ class width). Find the scale using a bar whose frequency AND width you know, then apply it to the others.
Source: CIE 0580 · Feb/March 2022 · Paper 4 · Q5b
Based on 3of 500+ insights extracted from CIE 0580 examiner reports (2018–2024).
Exam Coverage
This topic appears in the Cambridge IGCSE past papers. Our AI tutor can help with it on any question.
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Related Topics
Probability Basics
Basic probability introduces the scale from 0 to 1 and the idea of equally likely outcomes. Students calculate probabilities of single events, understand mutually exclusive events, and work with the probability that something does not happen.
Conditional Probability
Conditional probability deals with the likelihood of an event given that another event has already occurred. This topic uses tree diagrams, two-way tables and Venn diagrams to calculate P(A given B).
Combined Events
Combined events involve finding the probability of two or more things happening together or in sequence. Students use the addition rule for OR and the multiplication rule for AND, applying these to independent and dependent events.
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Probability trees, Venn diagrams, and data guides