GCSE & IGCSE maths practice

Probability questions and answers

Probability = number of ways it can happen ÷ total number of equally likely outcomes. Probabilities go from 0 (impossible) to 1 (certain), and all the outcomes add to 1, so $P(\text{not } A) = 1 - P(A)$ . Expected number of times $= P \times$ number of trials. Give answers as fractions, decimals or percentages.

8 questions · Foundation tier · Every answer is checked as you type it, with a full worked solution. Updated 27 Oct 2026.

Start the questions Probability: lesson Probability guide

Where probability comes up

GCSE (AQA, Edexcel, OCR)	Foundation and Higher: probabilities of single events, outcomes that sum to 1, expected outcomes, relative frequency and sample spaces.
Cambridge IGCSE (0580)	Core and Extended: probability of events, P(not A) = 1 − P(A), relative and expected frequencies, and sample space diagrams.

The method

P(event) = favourable outcomes ÷ total outcomes.
Probabilities of all outcomes add to 1.
Expected number = probability × trials.
Relative frequency = times it happened ÷ trials.

Probability questions

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Warm-up

Question 1Warm-upFoundation

A bag has 3 red, 5 blue and 2 green counters. One is taken at random. Find P(blue).

Question 2Warm-upFoundation

Using the same bag, find P(not red).

Exam-style

Question 3Exam-styleFoundation

A spinner lands on red (0.2), blue (0.35), green ( $x$ ) or yellow (0.15). Find $x$ .

Question 4Exam-styleFoundation

The probability of winning a game is 0.15. You play 60 times. How many times would you expect to win?

Question 5Exam-styleFoundation

A coin is flipped 50 times and lands on heads 37 times. What is the relative frequency of heads?

Question 6Exam-styleFoundation

Two fair dice are rolled and the scores added. Find the probability of a total of 7.

Challenge

Question 7ChallengeFoundation

A spinner has P(A) $= 2x$ , P(B) $= 3x$ and P(C) $= 0.5$ . Find P(A).

Question 8ChallengeFoundation

A bag has 12 counters and P(red) $= \tfrac{1}{3}$ . How many red counters must be added to make P(red) $= \tfrac{1}{2}$ ?

Common mistakes

Giving a probability greater than 1.
Writing probability as a ratio (1 : 3) instead of a fraction.
Forgetting some outcomes when listing a sample space.

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Sources

The questions are our own. The “where it comes up” notes are from each board's published specification, checked on 26 October 2026:

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