Knowledge Organiser: Tree Diagrams
Part of Tree Diagrams · GCSE GCSE Mathematics revision
This topic summary covers Knowledge Organiser: Tree Diagrams within Tree Diagrams for GCSE Mathematics. Revise Tree Diagrams in Probability for GCSE Mathematics with 15 exam-style questions and 20 flashcards. This is a high-frequency topic, so it is worth revising until the explanation feels precise and repeatable. It is section 7 of 7 in this topic. Use this topic summary to connect the idea to the wider topic before moving on to questions and flashcards.
Topic position
Section 7 of 7
Practice
15 questions
Recall
20 flashcards
Knowledge Organiser: Tree Diagrams
Key Terms
- Tree diagram: A visual tool showing all possible outcomes of multi-stage events
- Branch: A line representing one possible outcome at a stage
- Path: A route from start to end through the tree (one complete sequence)
- With replacement: Item returned before next draw — probabilities unchanged
- Without replacement: Item not returned — probabilities change at each stage
- Independent events: One event does not affect the probability of another
Must-Know Facts
- Probabilities on branches from the same point must add up to 1
- Multiply probabilities ALONG a path to get the probability of that sequence
- Add probabilities ACROSS paths that all lead to the same event
- Without replacement: after removing an item, total reduces by 1
- All final path probabilities must sum to 1 — use this to check
- Label every branch with both the outcome and its probability
Key Formulas
- P(path) = product of all branch probabilities along that path
- P(event) = sum of P(path) for every path where the event occurs
- P(A and B) = P(A) × P(B|A) — multiply along branches
- Check: sum of all path probabilities = 1
Common Mistakes
- Adding along branches instead of multiplying: To find P(path), MULTIPLY probabilities along the branches
- Multiplying instead of adding paths: For "either this path OR that path", ADD the path probabilities
- Not adjusting for "without replacement": If items are not replaced, the second branch probabilities change
- Branch probabilities not summing to 1: At each split, all branch probabilities must add to 1 — check this as you draw
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Practice Questions for Tree Diagrams
A fair coin is flipped twice. In a tree diagram, what must the probabilities on the branches from the same point always add up to?
Explain the two key rules used when calculating probabilities from a tree diagram. Your answer should refer to both the multiplication rule and the addition rule.
Quick Recall Flashcards
15 questions on Tree Diagrams — practise free
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