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Cambridge IGCSE Maths (0580) · Topic 8: Probability · 8.1

Cambridge IGCSE Maths 0580 Probability Questions

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.

Practise probability →Probability notes

What the syllabus asks

Summarised in our own words: check the exact wording in the official 0580 syllabus.

Probability questions: Core

For everyone: Core students (Papers 1 and 3) and Extended students (Papers 2 and 4).

Question 1 Core non-calculator · easy

A fair six-sided dice is rolled once.
Find the probability of rolling
(a) an even number
(b) a number greater than \(4\).

Show the worked answer
  1. (a) Even numbers: \(2, 4, 6\), so \(\frac{3}{6} = \frac{1}{2}\).
  2. (b) Greater than \(4\): \(5, 6\), so \(\frac{2}{6} = \frac{1}{3}\).

Answer: (a) \(\frac{1}{2}\) (b) \(\frac{1}{3}\)

Question 2 Core non-calculator · easy

The probability that it rains tomorrow is \(0.35\).
Find the probability that it does not rain tomorrow.

Show the worked answer
  1. \(P(\text{not } A) = 1 - P(A) = 1 - 0.35 = 0.65\)

Answer: \(0.65\)

Question 3 Core non-calculator · easy

A bag holds \(5\) red, \(3\) blue and \(2\) green counters. One counter is taken at random.
Find the probability that it is
(a) blue
(b) not red.

Show the worked answer
  1. There are \(10\) counters.
  2. (a) \(\frac{3}{10}\)
  3. (b) \(5\) are not red: \(\frac{5}{10} = \frac{1}{2}\).

Answer: (a) \(\frac{3}{10}\) (b) \(\frac{1}{2}\)

Question 4 Core calculator · easy · 2 marks

A fair six-sided dice is rolled. Find the probability of

(a) a prime number (b) a number greater than 4.

Show the answer and mark scheme
  • B1 (a) 3/6 oe
  • B1 (b) 2/6 oe

Answer: (a) \(\frac{1}{2}\) (b) \(\frac{1}{3}\)

Question 5 Core non-calculator · medium

A spinner lands on \(A\), \(B\), \(C\) or \(D\). \(P(A) = 0.2\), \(P(B) = 0.35\), \(P(C) = x\) and \(P(D) = 2x\).
Find \(x\) and \(P(D)\).

Show the worked answer
  1. The probabilities add to \(1\): \(0.2 + 0.35 + x + 2x = 1\).
  2. \(3x = 0.45\), so \(x = 0.15\) and \(P(D) = 0.3\).

Answer: \(x = 0.15\), \(P(D) = 0.3\)

Question 6 Core non-calculator · medium

Each letter of the word STATISTICS is written on a card. One card is chosen at random.
Find the probability that the letter is
(a) T
(b) a vowel.

Show the worked answer
  1. There are \(10\) letters: S, T, A, T, I, S, T, I, C, S.
  2. (a) There are \(3\) Ts: \(\frac{3}{10}\).
  3. (b) The vowels are A, I, I: \(\frac{3}{10}\).

Answer: (a) \(\frac{3}{10}\) (b) \(\frac{3}{10}\)

Question 7 Core non-calculator · medium · 2 marks

A spinner can land on red, blue, green or yellow. P(red) = 0.2, P(blue) = 0.35 and P(yellow) = 0.15. Find P(green).

Show the answer and mark scheme
  • M1 1 − (0.2 + 0.35 + 0.15)
  • A1 0.3

Answer: \(0.3\)

Question 8 Core calculator · medium · 3 marks

A bag contains only red and white counters. The probability of taking a red counter at random is \(\frac{3}{8}\). There are 15 white counters. How many red counters are there?

Show the answer and mark scheme
  • M1 P(white) = 5/8
  • M1 15 ÷ 5 × 8 = 24 counters
  • A1 9

Answer: \(9\)

Question 9 Core non-calculator · hard

A bag holds only red and blue beads. The probability of taking a red bead is \(\frac{3}{8}\). There are \(15\) blue beads.
How many red beads are in the bag?

Show the worked answer
  1. \(P(\text{blue}) = 1 - \frac{3}{8} = \frac{5}{8}\).
  2. \(\frac{5}{8}\) of the beads is \(15\), so there are \(24\) beads in total.
  3. Red beads: \(24 - 15 = 9\).

Answer: \(9\)

Examiner Insights: common mistakes in IGCSE Maths 0580, with fixes (our analysis of public sources) →

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).

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Questions students ask

Which Cambridge 0580 papers can test probability?

Probability is on both tiers (syllabus 8.1), so it can come up on Core Papers 1 (non-calculator) and 3 (calculator), and Extended Papers 2 (non-calculator) and 4 (calculator). Extended candidates also need the Extended parts listed on this page. Half of each tier's marks are on a non-calculator paper, so practise the non-calculator questions without one.

Are these Cambridge past-paper questions?

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.

Where can I practise more probability questions?

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.

More probability questions