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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 from 2025 to 2030 (Cambridge says the 2028–2030 syllabus has no significant changes that affect teaching). 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

8 questions written for 0580 in the Probability practice: 8 Core, 5 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) 12 (b) 45

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<0.65 (or 0.35<0.5)

Answer: (a) 0.65 (b) no, 0.35<0.65

0580 questions: Probability questions (Core and Extended, with worked answers)
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

8 questions written for 0580 in the Probability practice: 8 Core, 5 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, 3 marks):

A spinner is spun 80 times. It lands on red 26 times, blue 30 times and green 24 times.

(a) Write down the relative frequency of blue as a decimal.

(b) The spinner is spun 600 more times. Use the results to estimate how many times it lands on green.

Show the answer and mark scheme
  • B1 (a) 30/80 = 0.375
  • M1 (b) 24/80 × 600
  • A1 180

Answer: (a) 0.375 (b) 180

0580 questions: Relative and Expected Frequency questions (Core and Extended, with worked answers)
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

8 questions written for 0580 in the Probability practice: 7 Core and 1 Extended, 5 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) 14

Practice question (Extended, non-calculator, 4 marks):

A bag contains 5 red counters and 4 blue counters. Two counters are taken at random without replacement.

Find the probability that

(a) the counters are different colours

(b) at least one counter is blue.

Show the answer and mark scheme
  • M1 (a) 5/9 × 4/8 + 4/9 × 5/8
  • A1 40/72 = 5/9
  • M1 (b) 1 − 5/9 × 4/8
  • A1 52/72 = 13/18

Answer: (a) 59 (b) 1318

0580 questions: Combined Events and Tree Diagrams questions (Core and Extended, with worked answers)
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.

0580 practice questions

8 questions written for 0580 in the Probability practice: 8 Extended, 7 non-calculator, each with a Cambridge-style mark scheme (M method, A accuracy, B independent marks). Two of them:

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

60 students were asked how they travel to school.

WalkBusBoys1216Girls1814

A student who walks is chosen at random. Find the probability that the student is a girl.

Show the answer and mark scheme
  • M1 12 + 18 = 30 walk
  • A1 18/30 = 3/5

Answer: 35

Practice question (Extended, non-calculator, 4 marks):

200 adults were asked whether they prefer tea or coffee.

TeaCoffeeUnder 40356540 and over6040

Find the probability that

(a) an adult who prefers tea is 40 or over

(b) an adult under 40 prefers tea.

Show the answer and mark scheme
  • M1 (a) 35 + 60 = 95 prefer tea
  • A1 60/95 = 12/19
  • M1 (b) 35 out of 100
  • A1 7/20

Answer: (a) 1219 (b) 720

0580 questions: Conditional Probability questions (Core and Extended, with worked answers)
Edexcel 4MA1 notes: Probability
Practise (4MA1 questions, same mathematics): Tree Diagrams and Conditional Probability questions

Practise probability

32 practice questions are written for 0580 on every sub-topic of this topic. 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.

More on this topic

Try it now

1 of 5

  1. Question 1 of 5
  2. Question 2 of 5
  3. Question 3 of 5
  4. Question 4 of 5
  5. Question 5 of 5

5 quick questions on probability. No sign-in needed.

Two fair six-sided dice are rolled. Find the probability that the total is 9.
Choose your answer · keys 1–4

Knowledge organiser: Probability on one page (key facts, formulas and mistakes to avoid; printable PDF)

Questions about probability

What is in Cambridge IGCSE 0580 probability?

Topic 8 has 4 sub-topics: 8.1 Introduction to probability; 8.2 Relative and expected frequencies; 8.3 Probability of combined events; 8.4 Conditional probability.

Which probability sub-topics are Extended only?

8.4 Conditional probability. Core students (Papers 1 and 3) do not need them.

What do students get wrong in probability?

Combined events: adding where you should multiply. Our 0580 Examiner Insights page explains each one with a fix.

Are these notes free?

Yes. Every note and worked example on these pages is free to read, with no sign-in.

Join free: practise probability with marking →