Edexcel IGCSE Maths (4MA1) · Unit 6: Statistics & Probability
IGCSE Maths Probability 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 cover each solution and redo it yourself.
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: \(3+7=10\).
\(P(\text{blue})=\dfrac{7}{10}\).
Answer: \(\tfrac{7}{10}\)
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).
\(P=\dfrac{4}{20}=\dfrac{1}{5}\).
Answer: \(\tfrac{1}{5}\)
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 \(=\dfrac{23}{120}\).
Expected sixes \(=\dfrac{23}{120}\times600=115\).
Answer: \(\tfrac{23}{120}\); 115
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 \(3\times4=12\) outcomes.
Totals of 5: (1,4), (2,3), (3,2).
\(P=\dfrac{3}{12}=\dfrac{1}{4}\).
Answer: \(\tfrac{1}{4}\)
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: \(1-0.75=0.25\).
Answer: 0.75; 0.25
Tip: Only add probabilities when the events cannot happen together.
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.
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.
IGCSE Math Revision