Where can I download free probability PDF worksheets with answers?

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

What GCSE grade is probability (4V)?

Probability (topic code 4V) is a Grade 4 probability topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Probability Worksheets (PDF) with Answers — GCSE Maths

Free Probability PDF Worksheets & Answers

Grade 4 • Topic 4V

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & 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
Naiker Maths Exam question booklet & solutions	Qs	Ans
Dr Austin Practice grid / worksheet & answers	Qs	Ans
Maths4EveryOne GCSE 9–1 practice 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
The Maths Room Online topic notes & examples	Page
Cognito Interactive online lesson & practice	Page
MathsBot: horse race Interactive online resource	Open
esheets Self-marking online worksheet	Page

Grade 4 topics
4A - Compound interest	4B - Indices (index laws)
4C - Prime factors HCF and LCM	4D - Real life graphs
4E - Inequalities on a number line	4F - Solving inequalities
4G - Forming and solving equations	4H - nth term of a linear sequence
4J - Expanding and factorising	4K - Pythagoras theorem
4L - Angles in parallel lines	4M - Angles in polygons
4N - Surface area	4P - Volume of a cuboid
4Q - Volume of a prism	4R - Bearings
4S - Cylinders	4T - Plans and elevations
4U - Scatter graphs	4V - Probability
4W - Averages from tables	4X - Reverse mean
4Y - Area of a trapezium	4Z - Loci and construction

Explanation:

Probabilities must always be written as a fraction, decimal, or percentage between 0 and 1 (never write a probability as a ratio like 1 : 4 or in words). For mutually exclusive events (events that cannot happen at the same time), all probabilities in a table add up to 1, and P(not A) = 1 − P(A).

To find the expected number of successes in N trials, use the formula: Expected Frequency = Probability × Number of Trials.

Example 1: A biased spinner lands on Red, Blue, Green, or Yellow. P(Red) = 0.25, P(Blue) = 0.15, and P(Green) is twice P(Yellow). Find P(Green).

Solution:

Remaining probability = 1 − (0.25 + 0.15) = 0.60

Let P(Yellow) = x and P(Green) = 2x:

x + 2x = 0.60 → 3x = 0.60 → x = 0.20

P(Green) = 2 × 0.20 = 0.40 → Answer: 0.4

Example 2: The spinner in Example 1 is spun 300 times. Work out an estimate for the number of times it lands on Red.

Solution:

Expected frequency = P(Red) × Number of spins

= 0.25 × 300

= 75

Answer: 75 times

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Probability Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 OCR Nov 2022 2F Q19 / 5H Q3 3 marks

Full Paper (PDF) • Mark Scheme (PDF)

Azmi has a fair spinner numbered 2, 5 and 8.

(a) Complete the table to show all of the possible totals. [1 mark]

(b) Find the probability that the total is a square number. [2 marks]

Worked Solution & Mark Scheme (3 marks)

Part (a) Solution:

2 + 8 = 10
5 + 8 = 13
8 + 2 = 10. B1

Answer (a): Missing totals: 10 (row 2, col 8), 13 (row 5, col 8), 10 (row 8, col 2)

Part (b) Solution:

The 9 equally likely totals are 4, 7, 10, 7, 10, 13, 10, 13, 16 M1
The square numbers are 4 and 16 (2 outcomes out of 9) ⇒ probability = 2/9. A1

Answer (b): 29

Past Paper Example 2 AQA Nov 2024 1F Q9 6 marks

Full Paper (PDF) • Mark Scheme (PDF)

A number is picked at random from the first three positive odd numbers.
A number is picked at random from the first four prime numbers.
The two numbers are **multiplied** to get a score.

(a) Complete the table. [4 marks]

(b) What is the probability that the score is a square number?
Give your answer as a fraction. [2 marks]

Worked Solution & Mark Scheme (6 marks)

Part (a) Solution:

Odd numbers: 1, 3, 5. Prime numbers: 2, 3, 5, 7. Multiply each pair M3 A1

Answer (a): Headers 3 and 5; cells 2,3,5,7 / 6,9,15,21 / 10,15,25,35

Part (b) Solution:

Out of 12 outcomes, the square numbers are 9 and 25 (2 outcomes), giving 212 (or 16) M1 A1

Answer (b): Answer 212

Past Paper Example 3 AQA Jun 2023 2F Q18 / 2H Q7 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

In a game,
• an ordinary fair six-sided dice is rolled
• the fair spinner shown is spun.

The score is the dice number **substituted** into the spinner expression.

(a) Complete the table to show all of the possible scores.
@@TABULAR₀@@ [2 marks]

(b) A player wins the game if their score is 10 or more.
Work out the probability that they win the game. [1 mark]

Worked Solution & Mark Scheme (5 marks)

Part (a) Solution:

Substitute x = 1, 2, 3, 4, 5, 6 into 2x, 3x and x² M1 A1

Answer (a): Row 2x: 2, 4, 6, 8, 10, 12; Row 3x: 3, 6, 9, 12, 15, 18; Row x²: 1, 4, 9, 16, 25, 36

Part (b) Solution:

Scores ⩾ 10 are 10, 12 (in 2x), 12, 15, 18 (in 3x), and 16, 25, 36 (in x²) → 8 out of 18 = 8/18 (or 4/9) B1

Answer (b): Answer 818

Part (c) Solution:

711 × 8/18 = 711 × 4/9 = 316 M1 A1

Answer (c): Answer 316

← 4U Scatter graphs

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Probability

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Guide to Probability: Explanation, Diagrams & Worked Examples

GCSE Past Paper Probability Questions & Answers