GCSE Mathematics Revision — Tree Diagrams
Revise Tree Diagrams for GCSE Mathematics with a topic explanation, worked example and common mistakes. Check the board notes for specification differences.
At a glance
- What StudyVector is
- An exam-practice platform with board-aligned questions, explanations, and adaptive next steps.
- This topic
- Tree Diagrams in GCSE Mathematics: explanation, examples, and practice links on this page.
- Who it’s for
- Students revising GCSE Mathematics for UK exams.
- Exam boards
- Check your course page and the topic board notes for supported specifications.
- Free plan
- Sign up free to use tutor paths and feedback on your answers. Free access is Free daily revision · No card required. Pricing
- What makes it different
- Syllabus-shaped practice and progress tracking—not generic AI answers.
This page includes a topic explanation and a worked example. Check your course for current practice coverage.
Next in this topic area
Next step: Venn Diagrams & Sets
Continue in the same course — structured practice and explanations on StudyVector.
Go to Venn Diagrams & SetsTopic explanation
What 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 examples
Worked 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.
Practise this topic
Start with low-focus cards for Tree Diagrams, then move into full exam-style practice when you want the heavier session.
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
Check the available question sets for Tree Diagrams. Use your course and exam board to confirm which practice is relevant.
Tree Diagrams exam questionsGet help with Tree Diagrams
Get a personalised explanation for Tree Diagrams from the StudyVector tutor. Ask follow-up questions and work through problems with step-by-step support.
Open tutorSave your progress in Tree Diagrams
Start a free account for low-focus question cards, feedback and Play routes across available topics. Free daily limits apply; no card required.
Continue your revision
A public question for Tree Diagrams is still being reviewed. Your course page shows the topics currently available for practice.
Continue with Tree Diagrams
Create a free account to keep your course choice and save your practice progress.
Start free low-focus cardsAlready have an account? Log in
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).