Tree Diagrams — GCSE Mathematics Revision
Revise Tree Diagrams for GCSE Mathematics. Step-by-step explanation, worked examples, common mistakes and exam-style practice aligned to AQA, Edexcel and OCR.
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Go to Venn Diagrams & SetsWhat is Tree Diagrams?
Tree diagrams show all possible outcomes of two or more events. Each branch represents an outcome and is labelled with its probability. Branches from the same point must sum to 1. To find the probability of a combined outcome, multiply along the branches (AND). To find the probability of one outcome OR another, add the relevant combined probabilities.
Step-by-step explanationWorked example
A bag has 4 red and 6 blue balls. Two are picked without replacement. P(both red) = 4/10 × 3/9 = 12/90 = 2/15.
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Common mistakes
- 1Not adjusting probabilities for 'without replacement' — the denominator changes after each pick.
- 2Adding probabilities along branches instead of multiplying (AND = multiply along branches).
- 3Forgetting to include all relevant branches when calculating P(at least one).
- 4Branches from the same point not summing to 1.
Tree Diagrams exam questions
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Step-by-step method
Step-by-step explanation
4 steps · Worked method for Tree Diagrams
Core concept
Tree diagrams show all possible outcomes of two or more events. Each branch represents an outcome and is labelled with its probability. Branches from the same point must sum to 1. To find the probabil…
Frequently asked questions
What is the difference between with and without replacement?
With replacement: the item is put back, so probabilities stay the same for each pick. Without replacement: the item is not returned, so the total decreases and probabilities change.
How do I find P(at least one)?
It is often easier to calculate 1 - P(none). For example, P(at least one red) = 1 - P(no red).