Cambridge IGCSE Maths (0580) · Topic 8: Probability · 8.4
Conditional Probability questions with worked answers for Cambridge IGCSE Mathematics (0580). Each question says whether it is Core or Extended and whether it is for a calculator or non-calculator paper. Try each one before you open the answer.
Summarised in our own words: check the exact wording in the official 0580 syllabus.
Extended content, for Papers 2 and 4.
The table shows whether \(30\) students like tea.
A student who likes tea is chosen at random. Find the probability that the student is a girl.
| Likes tea | Does not like tea | |
|---|---|---|
| Boys | 5 | 7 |
| Girls | 9 | 9 |
Answer: \(\frac{9}{14}\)
In a group of \(50\) people, \(20\) are only in club \(A\), \(12\) are in both clubs, \(10\) are only in club \(B\) and \(8\) are in neither.
A person in club \(B\) is chosen at random. Find the probability that they are also in club \(A\).
Answer: \(\frac{6}{11}\)
\(P(A) = 0.4\) and \(P(A \cap B) = 0.12\).
Find \(P(B \mid A)\).
Answer: \(0.3\)
A box holds \(4\) red and \(6\) black cards. Two cards are taken at random without replacement.
The first card is red. Find the probability that the second card is also red.
Answer: \(\frac{1}{3}\)
The table shows how \(80\) students travel to school.
A Year 11 student is chosen at random. Find the probability that they walk.
| Walk | Bus | |
|---|---|---|
| Year 10 | 18 | 20 |
| Year 11 | 12 | 30 |
Answer: \(\frac{2}{7}\)
A fair six-sided dice is rolled. You are told the score is even.
Find the probability that the score is greater than \(3\).
Answer: \(\frac{2}{3}\)
The probability that Tom is late for school is \(0.2\). If he is late, the probability he gets a detention is \(0.5\); if he is not late, it is \(0.05\).
(a) Find the probability that Tom gets a detention.
(b) Tom gets a detention. Find the probability that he was late.
Answer: (a) \(0.14\) (b) \(\frac{5}{7}\)
A bag holds \(3\) red and \(2\) blue counters. Two are taken at random without replacement.
Given that at least one counter is red, find the probability that both are red.
Answer: \(\frac{1}{3}\)
Every question on this page is original, written for IGCSE Math Revision rather than taken from Cambridge papers, and each answer was re-solved independently before publishing. Questions with a mark scheme come from our 0580 practice bank (M method, A accuracy, B independent marks).
Conditional Probability is Extended content (syllabus 8.4), so it is tested only on the Extended papers, Paper 2 (non-calculator) and Paper 4 (calculator). Core candidates do not need it.
No. Every question here was written for IGCSE Math Revision in the style of the 0580 papers, and each answer was checked independently before publishing. For real exam practice, use the Cambridge past papers linked from our 0580 past papers page.
In the 0580 practice for topic 8 (Probability), where every question is marked and tagged Core or Extended. Practice is part of the IGCSE plan, with a free preview; the questions on this page are free.
IGCSE Math Revision