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

The 20 questions

1. What defines two events that are mutually exclusive?

   • Must occur together
   • Cannot occur together
   • Have equal probabilities
   • Sum to zero

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. What do the probabilities of a complete set of exhaustive outcomes sum to?

   • 0
   • 100
   • 1
   • 0.5

4. Which set of outcomes is exhaustive when rolling a standard six-sided dice?

   • 1 to 6
   • Even numbers only
   • 1 to 5
   • Odd numbers only

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 if a set of probability outcomes is exhaustive?

   • Outcomes are equal
   • Outcomes cannot overlap
   • Covers all outcomes
   • Outcomes are theoretical

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. Why do the probabilities of a set of mutually exclusive, exhaustive events sum to 1?

    • Events are independent
    • One must occur
    • All are equal
    • None can occur

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