Edexcel IGCSE Maths (4MA1) · Unit 6: Statistics & Probability

Edexcel IGCSE 4MA1 Probability: Exam Questions and Answers

Probability questions with full solutions for Pearson Edexcel International GCSE Mathematics A (4MA1), Higher tier. Read the 5 worked examples first, then try the 8 exam-style questions yourself and check your working against the mark scheme.

5 worked examples
8 questions with mark schemes
Higher tier · calculator allowed
Free, no sign-in

Practise probability in Unit 6 →Probability revision notes

What this topic covers

Basic probability: Working out the probability of simple events as fractions or decimals.
Probability 1: Theoretical Probability: Simple probability from equally likely outcomes.
Probability 2: Experimental & Relative Freq.: Estimating probability from a sample or frequency table.
Probability 4: Probability from Venn diagrams — union / intersection.
Probability 5: Mutually exclusive and independent event rules.

Probability worked examples

Worked example 1: Simple probability

A bag has 3 red and 7 blue beads. A bead is taken at random. Find the probability that it is blue.

Solution

Total beads: $3 + 7 = 10$ .
$P (blue) = \frac{7}{10}$ .

3 steps

Tip: Probabilities of all outcomes add to 1.

Worked example 2: Theoretical probability

Cards numbered 1 to 20 are shuffled. One is chosen. Find P(square number).

Solution

Square numbers: 1, 4, 9, 16 (4 outcomes).
$P = \frac{4}{20} = \frac{1}{5}$ .

3 steps · 1 to fill in

Tip: List the successful outcomes.

Worked example 3: Relative frequency

A dice is rolled 120 times and shows six 23 times. Estimate P(six) and the expected number of sixes in 600 rolls.

Solution

Relative frequency $= \frac{23}{120}$ .
Expected sixes $= \frac{23}{120} \times 600 = 115$ .

3 steps

Tip: Compare with 1/6 to judge whether the dice is fair.

Worked example 4: Sample space

Spinner A shows 1–3 and spinner B shows 1–4. Both are spun. Find P(total = 5).

Solution

There are $3 \times 4 = 12$ outcomes.
Totals of 5: (1,4), (2,3), (3,2).
$P = \frac{3}{12} = \frac{1}{4}$ .

4 steps · 1 to fill in

Tip: A sample space grid avoids missing outcomes.

Worked example 5: Mutually exclusive events

Events A and B are mutually exclusive with P(A) = 0.35 and P(B) = 0.4. Find P(A or B) and P(neither).

Solution

Mutually exclusive: add, $0.35 + 0.4 = 0.75$ .
Neither: $1 - 0.75 = 0.25$ .

3 steps · 1 to fill in

Tip: Only add probabilities when the events cannot happen together.

Where students lose marks on probability

Examiner's noteProbability tables: dividing the remainder by the wrong number

Where marks are lost: Candidates find 1 − (given probabilities) correctly but divide by 2 instead of the number of outcomes sharing it; conditional probability in context is weak.

Examiners flagged this in 2 exam series (November 2023, June 2024). Summarised in our own words from Pearson Edexcel examiner reports. Read the full note →

Probability exam-style questions

Try each question before you open the answer (one has its full worked solution open). The mark schemes use Edexcel-style marks: M for method, A for accuracy (after the method mark), B for an independent result.

Question 1 · easy · 2 marks

A bag contains 5 red, 7 blue and 8 green counters. One counter is taken at random. Find the probability that it is not blue.

Show the answer and mark scheme

M1 13 counters are not blue, or 1 − 7/20
A1 13/20 oe

Answer: $\frac{13}{20}$

Question 2 · medium · 3 marks

A bag holds only red, yellow and white beads. The probability of taking a red bead at random is 0.4. There are twice as many yellow beads as white beads, and there are 18 yellow beads. How many beads are in the bag?

Show the answer and mark scheme

M1 P(yellow) + P(white) = 0.6 and P(yellow) = 2 × P(white)
M1 P(yellow) = 0.4, so total = 18 ÷ 0.4
A1 45 cao

Answer: 45

Question 3 · medium · 4 marks

A biased spinner can land on 1, 2, 3 or 4. The probability that it lands on 1 is 0.2 and the probability that it lands on 2 is 0.35. It is twice as likely to land on 4 as on 3. (a) Find the probability that it lands on 3. (b) The spinner is spun 240 times. Work out an estimate for the number of times it lands on 4.

Show the answer and mark scheme

M1 0.2 + 0.35 + x + 2x = 1
A1 0.15
M1 240 × 0.3
A1 72

Answer: (a) 0.15 (b) 72

Question 4 · medium · 3 marks

Sana rolls a dice 150 times and gets a six 33 times. Ben rolls the same dice 50 times and gets a six 9 times. (a) Write down the relative frequency of a six in Sana's rolls. (b) Use all 200 rolls to work out the best estimate of the probability of a six.

Full worked solution Free, no sign-in

B1 0.22 oe
M1 (33 + 9) ÷ 200
A1 0.21 oe

Answer: (a) 0.22 (b) 0.21

Every question here has a full worked solution. See them all →

Question 5 · medium · 3 marks

$ξ = {whole numbers from 1 to 20}$ , A = {multiples of 3} and B = {factors of 36}. A number is chosen at random from $ξ$ . (a) Find $P (A \cap B)$ . (b) Find $P (A \cup B)$ .

Show the answer and mark scheme

M1 A ∩ B = {3, 6, 9, 12, 18}
A1 5/20 = 1/4 oe
B1 9/20 oe

Answer: (a) $\frac{1}{4}$ (b) $\frac{9}{20}$

Question 6 · medium · 3 marks

The probability that a bus is late on any day is 0.15, independently of other days. (a) Find the probability that the bus is late on Monday and not late on Tuesday. (b) Find the probability that the bus is not late on either day.

Show the answer and mark scheme

M1 0.15 × 0.85
A1 0.1275 oe
B1 0.7225 oe

Answer: (a) 0.1275 (b) 0.7225

Question 7 · hard · 4 marks

For two events A and B, $P (A) = 0.45$ , $P (B) = 0.3$ and $P (A \cup B) = 0.6$ . (a) Find $P (A \cap B)$ . (b) Find the probability that exactly one of the events A and B happens.

Show the answer and mark scheme

M1 0.45 + 0.3 − 0.6
A1 0.15
M1 0.6 − 0.15, or (0.45 − 0.15) + (0.3 − 0.15)
A1 0.45

Answer: (a) 0.15 (b) 0.45

Question 8 · very hard · 5 marks

Ali and Ben each take a driving test. The events 'Ali passes' and 'Ben passes' are independent. The probability that Ali passes is 0.8 and the probability that both pass is 0.56. (a) Find the probability that Ben passes. (b) Find the probability that exactly one of them passes. (c) Find the probability that at least one of them passes.

Show the answer and mark scheme

M1 0.56 ÷ 0.8
A1 0.7
M1 0.8 × 0.3 + 0.2 × 0.7
A1 0.38
B1 0.94 (1 − 0.2 × 0.3) ft their (a)

Answer: (a) 0.7 (b) 0.38 (c) 0.94

Every question and worked example here is original, written for IGCSE Math Revision rather than copied from Pearson papers, and each answer was re-solved independently before publishing.

Revise probability for the exam

Unit 6 practice: Statistics & Probability in the student hub (more questions with mark schemes)
IGCSE Maths revision notes for this topic and the IGCSE Maths formula sheet
Edexcel IGCSE Maths 4MA1 past papers to practise under exam conditions
IGCSE Maths 4MA1 examiner report summary: where students lose marks

Questions students ask

Which Edexcel IGCSE Maths papers test probability?

Either Higher tier paper, 1H or 2H, can test probability: both cover the whole Pearson Edexcel International GCSE Mathematics A (4MA1) specification and both allow a calculator. Show your method, because most marks are for working.

Where can I practise more probability questions?

In the IGCSE student hub: Unit 6 (Statistics & Probability) has more exam-style questions on this topic, each with a mark scheme. Practice starts with a 7-day free trial; the worked examples and questions on this page are free.

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Edexcel IGCSE 4MA1 Probability: Exam Questions and Answers

Try it first

What this topic covers

Probability worked examples

Worked example 1: Simple probability

Solution

Worked example 2: Theoretical probability

Solution

Worked example 3: Relative frequency

Solution

Worked example 4: Sample space

Solution

Worked example 5: Mutually exclusive events

Solution

Where students lose marks on probability

Probability exam-style questions

Question 1 · easy · 2 marks

Question 2 · medium · 3 marks

Question 3 · medium · 4 marks

Question 4 · medium · 3 marks

Full worked solution Free, no sign-in

Question 5 · medium · 3 marks

Question 6 · medium · 3 marks

Question 7 · hard · 4 marks

Question 8 · very hard · 5 marks

Revise probability for the exam

Questions students ask

Practise probability with your progress saved

More Unit 6 topics: Statistics & Probability