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Cambridge IGCSE Maths (0580) · Revision notes · Topic 8 of 9

Cambridge IGCSE Maths 0580 Probability Notes

Revision notes for topic 8, Probability, of the Cambridge IGCSE Mathematics (0580) syllabus for exams in 2025, 2026 and 2027. Each of the 4 sub-topics lists what the syllabus asks, marked Core or Extended, with a short explanation and a worked example. Cover the answer and try each example first.

Core Core students (Papers 1 and 3) learn the Core statements. Extended Extended students (Papers 2 and 4) learn everything: the Core statements, the Extended additions and the Extended-only sub-topics. Papers 1 and 2 are non-calculator.

8.1 Introduction to probability

Core C8.1 Extended E8.1

  • The probability scale from 0 to 1
  • Probability of a single event; P(not A) = 1 - P(A)

Same mathematics as Edexcel 4MA1.

0580 practice questions

6 questions written for 0580 in the Probability practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

A bag contains 3 red, 5 blue and 2 green counters. One counter is taken at random. Find

(a) P(blue) (b) P(not green)

Show the answer and mark scheme
  • B1 (a) 5/10 oe
  • B1 (b) 8/10 oe

Answer: (a) \(\frac{1}{2}\) (b) \(\frac{4}{5}\)

Practice question (Core, non-calculator, 2 marks):

The probability that it rains tomorrow is 0.35.

(a) Find the probability that it does not rain tomorrow.

(b) Is rain more likely than no rain? Give a reason.

Show the answer and mark scheme
  • B1 (a) 0.65
  • B1 (b) no, because \(0.35 \lt 0.65\) (or \(0.35 \lt 0.5\))

Answer: (a) \(0.65\) (b) no, \(0.35 \lt 0.65\)

Edexcel 4MA1 notes: Probability
Practise (4MA1 questions, same mathematics): Probability questions

8.2 Relative and expected frequencies

Core C8.2 Extended E8.2

  • Relative frequency as an estimate of probability
  • Expected frequency

Same mathematics as Edexcel 4MA1.

0580 practice questions

6 questions written for 0580 in the Probability practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

Ella throws a coin 50 times and gets 22 heads.

(a) Find the relative frequency of heads.

(b) How many heads would you expect in 300 throws of a fair coin?

Show the answer and mark scheme
  • B1 (a) 22/50 = 0.44
  • B1 (b) 150

Answer: (a) \(0.44\) (b) \(150\)

Practice question (Core, non-calculator, 2 marks):

The probability that Leo wins a game is 0.15. He plays the game 40 times. How many games should he expect to win?

Show the answer and mark scheme
  • M1 0.15 × 40
  • A1 6

Answer: \(6\)

Edexcel 4MA1 notes: Probability
Practise (4MA1 questions, same mathematics): Probability questions

8.3 Probability of combined events

Core C8.3 Extended E8.3

  • Combined events using sample space diagrams, Venn diagrams and tree diagrams

Extended also: Tree diagrams with and without replacement.

Same mathematics as Edexcel 4MA1.

Revise it

From our Edexcel 4MA1 Higher notes, so it may go beyond Core: Core students need only the Core statements above.

Multiply along the branches of a tree diagram, add the paths you want. Without replacement, the numbers on the second branches change.

Example: A bag has 3 red and 5 blue counters. Two are taken without replacement. P(both red)?

Answer: 3/8 × 2/7 = 6/56 = 3/28.

0580 practice questions

6 questions written for 0580 in the Probability practice: 6 Core, 3 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

Practice question (Core, non-calculator, 2 marks):

Two fair coins are thrown.

(a) List all the possible outcomes.

(b) Find the probability of two heads.

Show the answer and mark scheme
  • B1 (a) HH, HT, TH, TT
  • B1 (b) 1/4

Answer: (a) HH, HT, TH, TT (b) \(\frac{1}{4}\)

Practice question (Core, non-calculator, 2 marks):

A fair spinner numbered 1, 2 and 3 is spun and a fair coin is thrown.

(a) How many possible outcomes are there?

(b) Find the probability of a 3 and a head.

Show the answer and mark scheme
  • B1 (a) 6
  • B1 (b) 1/6

Answer: (a) \(6\) (b) \(\frac{1}{6}\)

Edexcel 4MA1 notes: Probability
Practise (4MA1 questions, same mathematics): Sets and Venn Diagrams questions · Probability questions · Tree Diagrams and Conditional Probability questions

8.4 Conditional probability

Extended only E8.4

Extended: Conditional probability from Venn diagrams, tree diagrams and tables.

Same mathematics as Edexcel 4MA1.

Edexcel 4MA1 notes: Probability
Practise (4MA1 questions, same mathematics): Tree Diagrams and Conditional Probability questions

Practise probability

18 practice questions are written for 0580 on 8.1, 8.2, 8.3. For the 4 sub-topics that are the same mathematics in Edexcel 4MA1, the practice also has our 4MA1 Higher questions, which are Extended level. Core students: use the Core filter on the practice page; every sub-topic with Core content has questions written for 0580 Core. Practice is part of the IGCSE plan, with a free preview; these notes are free.