Where can I download free probability trees PDF worksheets with answers?

On this MathsLinks page you can download free printable probability trees PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Maths Genie, Maths4Everyone, Corbett Practice, Corbett Textbook, plus a printable one-page probability trees revision guide.

What GCSE grade is probability trees (5W)?

Probability trees (topic code 5W) is a Grade 5 probability topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Probability trees Worksheets (PDF) with Answers — GCSE Maths

Free Probability trees PDF Worksheets & Answers

Grade 5 • Topic 5W

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Maths4Everyone GCSE 9–1 practice booklet & solutions	Qs	Ans
Corbett Practice Practice Questions & answers	Qs	Ans
Corbett Textbook Textbook Exercise & answers	Qs	Ans
Maths Made Easy MME worksheet & model answers	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
1st Class Maths (Edxl) Edexcel exam questions & solutions	Qs	Ans
1st Class Maths (AQA) AQA exam questions & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
Naiker Maths Exam question booklet & solutions	Qs	Ans
Metatutor Topic worksheet & worked solutions	Qs	Ans
GCSE Maths Rocket Practice questions & answers	Qs	Ans
E Classroom GCSE topic booklet & answers	Qs	Ans
PMT (Edxl) Edexcel GCSE topic questions & solutions	Qs	Ans
PMT (AQA) AQA GCSE topic questions & solutions	Qs	Ans
PMT (IGCSE) Edexcel IGCSE topic questions & solutions	Qs	Ans
Cognito Interactive online lesson & practice	Page
esheets Self-marking online worksheet	Page

Grade 5 topics
5A - Combining ratios	5B - Direct and inverse proportion
5C - Reverse percentages	5D - Standard form
5E - Speed	5F - Changing the subject
5G - Quadratic expressions	5H - Solving quadratic equations
5J - Drawing quadratic graphs	5K - Cubic/reciprocal graphs
5L - Simultaneous equations	5M - Sector areas and arc lengths
5N - Sim. equ. graphically	5P - Midpoint of a line segment
5Q - Gradient of a line	5R - Equation of a line
5S - Spheres and cones	5T - Similar shapes (lengths)
5U - Trigonometry (SOHCAHTOA)	5V - Exact trig. values
5W - Probability trees	5X - Vectors
5Y - Venn diagrams	5Z - Density
5AA - Pressure

Explanation:

On a probability tree diagram, each pair of branches from the same point must add up to 1. Multiply along the branches for AND (P(A and B) = P(A) × P(B)), and add the end probabilities together when more than one path satisfies the question (OR).

Check whether items are picked with replacement (second-pick probabilities stay the same) or without replacement (reduce total denominator by 1 on the second branches, and reduce the numerator by 1 if that colour was already picked).

Example 1: The probability Sam passes his theory test is 0.8 and practical test is 0.6. Find the probability he passes only one test.

Solution:

P(P, F) = 0.8 × 0.4 = 0.32; P(F, P) = 0.2 × 0.6 = 0.12

Answer: 0.32 + 0.12 = 0.44

Example 2: A bag has 5 red and 3 blue counters. Two are picked without replacement. Find P(both same colour).

Solution:

P(Red, Red) = 58 × 47 = 2056

P(Blue, Blue) = 38 × 27 = 656

Total = 2056 + 656 = 2656 = 1328

Answer: 1328

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Probability trees Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 Eduqas Jun 2024 2F Q19 / 2H Q4 4 marks

Full Paper (PDF) • Mark Scheme (PDF)

For her lunch, Gina sometimes eats a salad and sometimes drinks a coffee.
The probability she eats a salad for lunch on a given day is 0.4.
The probability she drinks a coffee on a given day is 0.25.
Eating a salad for lunch and drinking a coffee are independent.

(a) Complete the following tree diagram. [2 marks]

(b) Calculate the probability that, on a given day, Gina does not eat a salad for lunch but does drink a coffee. [2 marks]

Worked Solution & Mark Scheme (4 marks)

Part (a) Solution:

P(does not eat salad) = 1 - 0.4 = 0.6. M1
Since drinking coffee is independent: P(drinks coffee) = 0.25, P(does not drink coffee) = 1 - 0.25 = 0.75 on both salad and no-salad branches. A1

Answer (a): P(not salad) = 0.6; P(coffee) = 0.25 and P(not coffee) = 0.75 on both branch sets.

Part (b) Solution:

P(No salad AND Drinks coffee) = 0.6 × 0.25 = 0.15 M1 A1

Answer (b): 0.15

Past Paper Example 2 GCSE Jun 2025 2H Q11 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

Freya and Ria each do an exam.
The probability that Freya will pass the exam is 0.8
The probability that Ria will pass the exam is 0.85

(a) Complete the probability tree diagram. [2 marks]

(b) Work out the probability that only one of Freya or Ria will pass the exam. [3 marks]

Worked Solution & Mark Scheme (5 marks)

Part (a) Solution:

Freya fail = 1 – 0.8 = 0.2. Ria fail = 1 – 0.85 = 0.15 M1 A1

Answer (a): Tree completed (Freya fail = 0.2, Ria pass = 0.85, Ria fail = 0.15)

Part (b) Solution:

P(Freya pass, Ria fail) = 0.8 × 0.15 = 0.12 M1
P(Freya fail, Ria pass) = 0.2 × 0.85 = 0.17 M1
P(only one) = 0.12 + 0.17 = 0.29 A1

Answer (b): 0.29

Past Paper Example 3 AQA Jun 2024 3H Q12 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

Cards are either gold or not gold.
P(gold) = 0.05
Harim chooses a card at random and replaces it.
He then chooses a second card.

(a) Complete the tree diagram. [2 marks]

(b) What is the probability that **at least one** of Harim’s cards is gold? [3 marks]

Worked Solution & Mark Scheme (5 marks)

Part (a) Solution:

P(Not gold) = 1 – 0.05 = 0.95 M1 A1

Answer (a): First card Not gold = 0.95; Second card branches: 0.95, and 0.05 / 0.95

Part (b) Solution:

P(both not gold) = 0.95 × 0.95 = 0.9025 M2
P(at least one gold) = 1 – 0.9025 = 0.0975 A1

Answer (b): Answer 0.0975

← 5V Exact trig. values

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Probability trees

Free Probability trees PDF Worksheets & Answers

Guide to Probability trees: Explanation, Diagrams & Worked Examples

GCSE Past Paper Probability trees Questions & Answers