IGCSE Maths Tree Diagrams Notes
Tree diagrams show combined events branch by branch. Multiply along branches and add the paths that satisfy the outcome.
Key concepts
- Branches
- Each set of branches shows the outcomes of one event, with probabilities summing to 1.
- Multiply along
- Multiply the probabilities on a path to find P(that combination).
- Add across
- Add the path probabilities for all ways an outcome can occur.
Key formulas
Path probability
P(path) = product of branch probabilities
Worked example
A coin is flipped twice. Find P(two heads).
- 1P(head) each flip = 1/2.
- 2Multiply along the head–head path: 1/2 × 1/2.
- 3State the result.
Answer: 1/4
Common mistakes
✗ Branch probabilities not summing to 1.
✓ Check each pair (or set) of branches totals 1.
✗ Not reducing totals 'without replacement'.
✓ Lower the denominator on the second set of branches.
✗ Forgetting to add multiple paths.
✓ Add all paths that give the required outcome.
Quick check
Try these, then reveal the answers.
P(HH) on two fair coins?Reveal answer
1/4
P(at least one head) in two flips?Reveal answer
3/4
Along a branch you… ?Reveal answer
Multiply
Exam tips
- Label every branch with its probability before calculating.
- For 'at least one', use 1 − P(none).
- Take care to change probabilities when there is no replacement.
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Frequently asked questions
Do I multiply or add on a tree diagram?+
Multiply along the branches of a single path; add the results of the different paths that give the outcome.
What changes when it is 'without replacement'?+
The total (and the count of the item removed) decreases, so the second-branch probabilities change.
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