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Tree diagrams and combined events

Tree Diagrams

38 self-marking GCSE and IGCSE practice questions on Tree Diagrams, written specifically for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Core and Extended tier. Instant marking with full worked solutions on every question.

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Sample Tree Diagrams questions

A few of the 38 questions, from easier to harder. Choose your exam board and tier to practise them, with every answer marked.

Question 16 marksGrade 4
Ryan shoots an arrow at a target, then kicks a ball at a goal. P(hits target) = 2/3. P(scores a goal) = 3/5, independent of the target result. (a) Complete the tree diagram with all branch probabilities. (a)(i) P(miss). (a)(ii) P(not score). (b)(i) Find the probability that Ryan misses the target and does not score a goal. (b)(ii) Find the probability that Ryan either hits the target or scores a goal or both.
Show the worked solution
(a) P(miss) = 1 − 2/3 = 1/3. P(not score) = 1 − 3/5 = 2/5. M1 (1 correct answer)

What are the common mistakes in Tree Diagrams?

When a pupil makes one of these on Revision Workshop, the marking engine names the mistake and explains it, instead of just marking the answer wrong.

Calculates the probability of both events occurring instead of exactly one occurring
Calculated P(both black) instead of P(exactly one black).
Counts only one ordering of a combined event (e.g. Win-then-Lose) when "exactly one" outcomes require adding both orderings
Only calculated one route (e.g. black then white) and forgot to also add the reverse order.
Uses addition where the correct operation was multiplication
Added the two branch probabilities instead of multiplying along the branches.

Quick answers about Tree Diagrams

How many Tree Diagrams practice questions are there?: There are 38 self-marking GCSE and IGCSE Maths questions on Tree Diagrams, written for AQA, Pearson, OCR, Pearson International GCSE Maths A (4MA1), Cambridge IGCSE Mathematics (0580), Cambridge IGCSE (9-1) Mathematics (0980) across Foundation and Higher and Core and Extended tier. Each one is marked instantly and has a full worked solution.
Do I need an account to practise Tree Diagrams?: No. You can start practising Tree Diagrams straight away without an account. A free account keeps your results across sessions, so you can see your progress on this topic over time.