GCSE Maths (AQA) chapter 5: Probability MCQs with answers

By Team Megalecture · Updated 4 Nov 2026

20 exam-style questions on Probability, each with the answer and a short explanation. Ten of them are below to try. The chapter test draws ten fresh questions each time and is marked the moment you finish, with your score by topic.

20 questions · 2 topics · 10 per test

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What chapter 5 covers

Ten Probability questions with answers

Try each one, then open the answer. These ten stay the same; the test draws new ones every time.

1. A and B are independent events with P(A) = 0.3 and P(B) = 0.6. What is P(A and B)?

  1. A
    0.9
  2. B
    0.72
  3. C
    0.18
  4. D
    0.09
Show answer

Answer: C. For independent events multiply: 0.3 × 0.6 = 0.18. Adding (0.9) is for mutually exclusive events with "or".

2. A bag holds only red, blue and green balls. P(red) = 0.35 and P(blue) = 0.4. What is P(green)?

  1. A
    0.25
  2. B
    0.75
  3. C
    0.14
  4. D
    0.65
Show answer

Answer: A. The probabilities of all outcomes add to 1: 1 − 0.35 − 0.4 = 0.25. 0.75 is P(red or blue).

3. Calculator. The probability that it rains today is 0.4. If it rains today, the probability it rains tomorrow is 0.7; if not, it is 0.3. Given that it rains tomorrow, what is the probability that it rained today, to 3 decimal places?

  1. A
    0.609
  2. B
    0.280
  3. C
    0.700
  4. D
    0.400
Show answer

Answer: A. P(rain tomorrow) = 0.28 + 0.18 = 0.46. P(rain today | rain tomorrow) = 0.28 ÷ 0.46 = 0.609. 0.7 is the probability the other way round.

4. Two fair six-sided dice are rolled and the scores are added. What is the probability of a total of 8?

  1. A
    1/6
  2. B
    5/36
  3. C
    1/9
  4. D
    1/12
Show answer

Answer: B. There are 36 equally likely outcomes, and 8 comes from (2, 6), (3, 5), (4, 4), (5, 3), (6, 2): 5 outcomes, so 5/36. Forgetting that (2, 6) and (6, 2) are different gives too few.

5. A bag has 5 red and 3 blue counters. Two counters are taken at random without replacement. What is the probability that they are different colours?

  1. A
    15/28
  2. B
    15/56
  3. C
    15/32
  4. D
    1/2
Show answer

Answer: A. P(red then blue) + P(blue then red) = 5/8 × 3/7 + 3/8 × 5/7 = 30/56 = 15/28. 15/56 counts only one of the two orders.

6. In a group of 50 people, 28 like tea, 22 like coffee and 9 like both. How many like neither?

  1. A
    0
  2. B
    18
  3. C
    9
  4. D
    41
Show answer

Answer: C. Tea or coffee = 28 + 22 − 9 = 41, so 50 − 41 = 9 like neither. Adding 28 + 22 = 50 counts the 9 who like both twice.

7. A fair spinner numbered 1 to 4 is spun and a fair coin is thrown. What is the probability of an even number and heads?

  1. A
    1/2
  2. B
    1/8
  3. C
    1/4
  4. D
    3/4
Show answer

Answer: C. The sample space has 4 × 2 = 8 outcomes, and (2, H) and (4, H) are the successful ones: 2/8 = 1/4. Also ½ × ½ = ¼.

8. A bag has 5 red and 3 blue counters. Two counters are taken at random without replacement. What is the probability that both are red?

  1. A
    25/64
  2. B
    15/56
  3. C
    5/16
  4. D
    5/14
Show answer

Answer: D. 5/8 × 4/7 = 20/56 = 5/14. After one red is taken there are 4 red out of 7 left. 25/64 assumes the first counter is replaced.

9. In a class of 60, there are 25 boys and 35 girls. 18 of the boys and 14 of the girls own a bike. A bike owner is chosen at random. What is the probability that it is a boy?

  1. A
    18/25
  2. B
    9/16
  3. C
    3/10
  4. D
    5/12
Show answer

Answer: B. There are 18 + 14 = 32 bike owners, and 18 are boys: 18/32 = 9/16. 18/25 is the probability that a boy owns a bike.

10. A bag contains only red and blue counters. The probability of taking a red counter is 3/8. There are 15 red counters. How many blue counters are there?

  1. A
    40
  2. B
    9
  3. C
    24
  4. D
    25
Show answer

Answer: D. 3/8 of the total is 15, so the total is 40 and there are 40 − 15 = 25 blue counters. 40 is the total, not the blue counters.

Start the chapter testAbout the GCSE Maths (AQA) test

Read the notes for this chapter

Ways to practise this chapter

Probability: questions students ask

How many Probability MCQs are there?

20, each with the answer and a short explanation, across 2 topics: P1–P5 Probability and expected outcomes, P6–P9 Combined events and conditional probability. Every chapter test draws ten of them, so you can take it many times.

Is the GCSE Maths (AQA) chapter 5 test free?

Yes. The test, the answers and the explanations are free and need no sign-up. Sign in only if you want your scores kept across devices.

How is the chapter test marked?

The moment you press Finish: your score, the right answer and an explanation for every question, and the ones you got wrong saved in My mistakes to retry.

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