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, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP.
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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.
Mini lesson for Tree Diagrams
1. Understand the core idea
Tree diagrams show all possible outcomes of two or more events. Each branch represents an outcome and is labelled with its probability.
Can you explain Tree Diagrams without copying the notes?
2. Turn it into marks
A bag has 4 red and 6 blue balls. Two are picked without replacement.
Underline the method, evidence, or command-word move that would earn credit in GCSE Probability.
3. Fix the likely mark leak
Watch for this mistake: Not adjusting probabilities for 'without replacement' — the denominator changes after each pick.
Write one correction rule before doing another practice question.
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Tree Diagrams practice questions
These are original StudyVector questions for revision practice. They are not official exam-board questions.
Question 1
In one GCSE sentence, explain what Tree Diagrams is testing.
Answer: Tree diagrams show all possible outcomes of two or more events. Each branch represents an outcome and is labelled with its probability.
Mark focus: Precise definition and topic focus.
Question 2
A student sees a Tree Diagrams question but is not sure how to start. What should the first method line establish?
Answer: It should identify the rule, equation, diagram feature, or transformation before any calculation. That protects method marks and makes later checking easier.
Mark focus: Method selection and command-word control.
Question 3
A student makes this mistake: "Not adjusting probabilities for 'without replacement' — the denominator changes after each pick." What should their next repair task be?
Answer: Do one Tree Diagrams question and review the mistake type.
Mark focus: Error correction and next-step practice.
Tree Diagrams flashcards
Core idea
What is the main idea in Tree Diagrams?
Tree diagrams show all possible outcomes of two or more events. Each branch represents an outcome and is labelled with its probability.
Common mistake
What mistake should you avoid in Tree Diagrams?
Not adjusting probabilities for 'without replacement' — the denominator changes after each pick.
Practice
What is one useful practice task for Tree Diagrams?
Answer one Tree Diagrams question and review the mistake type.
Exam board
How should you use board notes for Tree Diagrams?
Use your own GCSE specification for exact paper wording and depth.
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
Exam-style questions for Tree Diagrams with mark-scheme style solutions and timing practice. Aligned to AQA, Edexcel, OCR, WJEC, Eduqas, CCEA, Cambridge International (CIE), SQA, IB, AP specifications.
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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).