Lesson P4

P4 Exhaustive and mutually exclusive outcomes sum to 1 Quiz: AQA Maths, Unit 5

20 questions

Written by Revision Ninja · Last reviewed 11 October 2026

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Lesson P4, Exhaustive and mutually exclusive outcomes sum to 1: 20 multiple choice questions for the AQA GCSE Maths (8300), Unit 5: Probability, written with Revision Ninja.

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The 20 questions

  1. When are outcomes mutually exclusive?

    • They always happen together in the same trial
    • They cannot both occur at the same time
    • They are equally likely to occur in each trial
    • Each has probability of exactly 0.5 per trial

  2. Outcomes A, B and C are exhaustive and mutually exclusive. P(A) = 0.3 and P(B) = 0.5. What is P(C)?

    • 0.2
    • 0.15
    • 0.8
    • 0.5

  3. The probabilities of an exhaustive set of outcomes add up to what?

    • 0
    • 100
    • 1
    • the number of trials

  4. Which set of outcomes is exhaustive for rolling a fair dice?

    • All numbers from 1 to 6
    • Only 1 and 6
    • Only the prime numbers
    • Only the even numbers

  5. A spinner has four sections with probabilities 0.1, 0.2, 0.3 and x. What is x?

    • 0.3
    • 0.4
    • 0.1
    • 0.6

  6. What does it mean for a list of outcomes to be exhaustive?

    • No outcomes are included in the list at all
    • Each outcome appears twice in the results list
    • The list covers every possible outcome
    • The outcomes overlap with one another in a list

  7. If events A and B are mutually exclusive, what is P(A or B)?

    • P(A) - P(B)
    • P(A) + P(B)
    • P(A) / P(B)
    • P(A) x P(B)

  8. What is the probability of not A?

    • 1 + P(A)
    • 2 - P(A)
    • P(A) - 1
    • 1 - P(A)

  9. A spinner has P(red) = 0.35, P(blue) = 0.4 and P(green) = 0.25. What is the probability of not blue?

    • 0.75
    • 0.4
    • 0.25
    • 0.6

  10. A bag has only red, blue and yellow counters. P(red) = 1/3 and P(blue) = 1/2. What is P(yellow)?

    • 1/6
    • 1/3
    • 5/6
    • 1/2

  11. A spinner has probabilities 0.12, 0.18, 0.2 and 0.1 for four outcomes, plus a fifth x. What is x?

    • 0.4
    • 0.6
    • 0.3
    • 0.25

  12. For a game, P(win) = 0.07 and P(lose) = 0.58. What is P(draw)?

    • 0.35
    • 0.58
    • 0.07
    • 0.65

  13. The probability of rain is 0.6 and of sun is 0.25. What is the probability of any other weather?

    • 0.6
    • 0.4
    • 0.85
    • 0.15

  14. A fair dice is rolled. What is the probability of getting a 1 or a 2?

    • 1/3
    • 1/2
    • 1/6
    • 2/3

  15. A coin has P(heads) = 0.45 and the outcomes are exhaustive. What is P(tails)?

    • 0.1
    • 0.55
    • 0.45
    • 0.5

  16. Mutually exclusive and exhaustive events A, B and C have P(A) = 2x, P(B) = x and P(C) = x. What is x?

    • 0.5
    • 0.2
    • 0.25
    • 0.4

  17. (H) Events A, B and C are exhaustive and mutually exclusive, with P(A) = 0.2, P(B) = 2x and P(C) = 3x. What is x?

    • 0.8
    • 0.4
    • 0.2
    • 0.16

  18. (H) A spinner has exhaustive mutually exclusive outcomes with probabilities 1/4, 1/4, 1/8 and y. What is y?

    • 1/8
    • 5/8
    • 3/8
    • 1/2

  19. (H) Events A and B are mutually exclusive and exhaustive, and P(A) = 0.7. What is P(B)?

    • 1.7
    • 0.3
    • 0.7
    • 0.5

  20. (H) Why must the probabilities of an exhaustive set of outcomes sum to one?

    • The sum counts the number of trials that were carried out
    • One outcome must occur, so the total probability is certainty
    • Probabilities in an exhaustive set are always equal to halves
    • Each outcome must have probability one, so the total is larger

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