Where can I download free probability equation questions PDF worksheets with answers?

On this MathsLinks page you can download free printable probability equation questions PDF worksheets (Qs) and full worked solutions or mark schemes (Ans) from Ken Stafford, Maths Genie, Dr Frost, Dr Austin, E Classroom, plus a printable one-page probability equation questions revision guide.

What GCSE grade is probability equation questions (8L)?

Probability equation questions (topic code 8L) is a Grade 8+ probability topic in GCSE Maths for Edexcel, AQA, OCR, Eduqas and IGCSE specifications.

Free Probability equation questions Worksheets (PDF) with Answers — GCSE Maths

Free Probability equation questions PDF Worksheets & Answers

Grade 8+ • Topic 8L

Resource	Questions	Answers
Ken Stafford GCSE past paper questions & solutions	Qs	Ans
Maths Genie Graded exam questions & solutions	Qs	Ans
Dr Frost GCSE worksheet & solutions	Qs	Ans
Dr Austin (1) Practice grid / worksheet & answers	Qs	Ans
Dr Austin (2) Practice grid / worksheet & 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

Grade 8+ topics
8A - Quad. sim. equations	8B - Transforming graphs y=f(x)
8C - Algebraic proof	8D - Completing the square
8E - Quadratic inequalities	8F - Quadratic sequences
8G - Velocity time graphs	8H - Circles and tangents
8J - Circle theorem proof	8K - Vector proof
8L - Probability equation questions	8M - Invariant points
8N - Spheres, cones and cylinders	8P - Volume of a frustum

Explanation:

Algebraic probability questions give the number of counters in terms of n or x (or a ratio) and state the numerical probability of a two-step event without replacement. Write the branch probabilities as algebraic fractions, remembering to subtract 1 from the total denominator on the second pick.

Multiply (and add if there are multiple valid paths), equate your algebraic fraction to the given probability, cross-multiply to clear fractions, and rearrange into a quadratic equation an² + bn + c = 0. Always reject negative or non-integer roots.

Example 1: A bag has n red counters and 3 blue counters. Two are taken without replacement. Given P(both red) = 514, find n.

Solution:

nn + 3 × n − 1n + 2 = 514 ⇒ 14n(n − 1) = 5(n + 3)(n + 2)

3n² − 13n − 10 = 0 ⇒ (3n + 2)(n − 5) = 0 ⇒ Answer: n = 5

Example 2: A bag has x green and (10 − x) yellow balls. Two are picked without replacement. Given P(both green) = 13, find x.

Solution:

Total balls = 10: P(GG) = x10 × x − 19 = 13

x(x − 1)90 = 13 ⇒ x² − x = 30

x² − x − 30 = 0 ⇒ (x − 6)(x + 5) = 0

Answer: x = 6

Scanned GCSE Exam Questions & Worked Solutions

GCSE Past Paper Probability equation questions Questions & Answers

10-Question Interactive Quiz More Past Paper Questions

Past Paper Example 1 IGCSE Jan 2020 2HR Q16 2 marks

Full Paper (PDF) • Mark Scheme (PDF)

Cody has two bags of counters, bag **A** and bag **B**.
Each of the counters has either an odd number or an even number written on it.
There are 10 counters in bag **A** and 7 of these counters have an **odd** number written on them.
There are 12 counters in bag **B** and 7 of these counters have an **odd** number written on them.
Cody is going to take at random a counter from bag **A** and a counter from bag **B**.

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

Worked Solution & Mark Scheme (2 marks)

Part (a) Solution:

Bag A Even = 3/10 M1
Bag B branches = 7/12 Odd, 5/12 Even A1

Answer (a): Bag A: 3/10; Bag B: 7/12, 5/12 and 7/12, 5/12

Past Paper Example 2 IGCSE Jun 2023 1FR Q28 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

Moeen has a biased 6-sided dice.
The table gives information about the probability that, when the dice is thrown, it will land on each number.

(a) Show that x + y = 0.19 [2 marks]

(b) work out the value of x and the value of y
Show clear algebraic working. [3 marks]

Worked Solution & Mark Scheme (5 marks)

Part (a) Solution:

1 – (0.15 + 0.5 + 0.13 + 0.03) = 1 – 0.81 = 0.19 M1 C1

Answer (a): x + 0.15 + 0.5 + y + 0.13 + 0.03 = 1 ⇒ x + y + 0.81 = 1 ⇒ x + y = 0.19

Part (b) Solution:

Adding equations: 4x = 0.28 ⇒ x = 0.07 M2
y = 0.19 – 0.07 = 0.12 A1

Answer (b): x = 0.07, y = 0.12

Past Paper Example 3 GCSE Jun 2018 3F Q24 5 marks

Full Paper (PDF) • Mark Scheme (PDF)

There are some counters in a bag.
The counters are red or white or blue or yellow.
Bob is going to take at random a counter from the bag.
The table shows each of the probabilities that the counter will be blue or will be yellow.

There are 18 blue counters in the bag.
The probability that the counter Bob takes will be red is twice the probability that the counter will be white.

(a) Work out the number of red counters in the bag. [4 marks]

(b) Explain why. [1 mark]

Worked Solution & Mark Scheme (5 marks)

Part (a) Solution:

P(red) + P(white) = 1 – (0.45 + 0.25) = 0.30 ⇒ P(red) = 0.20, P(white) = 0.10 M2
Total counters = 18 ÷ 0.45 = 40 M1
Red counters = 0.20 × 40 = 8 A1

Answer (a): 8

Part (b) Solution:

Because half (0.5) of the total number of marbles must be a whole number

Answer (b): Because half (0.5) of the total number of marbles must be a whole number

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