M1 Mutually exclusive and independent events Quiz: AQA Maths, Unit 11

The 20 questions

1. Events A and B are mutually exclusive. Which statement is always true?

   • P(A) = P(B)
   • P(A or B) = 0
   • P(A given B) = P(A)
   • P(A and B) = 0

2. Events A and B are independent. Which expression gives P(A and B)?

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

3. For mutually exclusive events A and B, which formula gives P(A or B)?

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

4. For two events with non-zero probabilities, can they be both mutually exclusive and independent?

   • Uncertain
   • Sometimes
   • Always
   • Never

5. P(A) = 0.4 and P(B) = 0.25, with A and B independent. What is P(A and B)?

   • 0.15
   • 0.65
   • 0.10
   • 0.04

6. P(A) = 0.6 and P(B) = 0.2, with A and B mutually exclusive. What is P(A or B)?

   • 0.12
   • 0.68
   • 0.40
   • 0.80

7. P(A) = 0.3 and P(B) = 0.6, with A and B independent. What is P(A or B)?

   • 0.42
   • 0.90
   • 0.72
   • 0.18

8. If P(A) = 0.5, P(B) = 0.4 and P(A or B) = 0.7, how are events A and B related?

   • Complementary
   • Dependent
   • Independent
   • Mutually exclusive

9. A fair coin is tossed and a fair six-sided die is rolled. What is the probability of a head and a six?

   • 1/6
   • 1/2
   • 7/12
   • 1/12

10. One card is drawn from a standard 52-card pack. What is the probability it is a king or a queen?

    • 1/26
    • 2/13
    • 4/13
    • 1/13

11. P(A) = 0.2 and P(B) = 0.3, with A and B independent. What is the probability that neither A nor B occurs?

    • 0.50
    • 0.06
    • 0.56
    • 0.44

12. A and B are independent with P(A) = 0.5 and P(B) = 0.2. What is P(A or B)?

    • 0.30
    • 0.70
    • 0.60
    • 0.10

13. Events A and B are independent with P(A) = 0.9 and P(B) = 0.8. What is the probability that exactly one of them occurs?

    • 0.72
    • 0.98
    • 0.74
    • 0.26

14. Given P(A) = 0.7, P(B) = 0.5 and P(A and B) = 0.35, how are A and B related?

    • Independent
    • Mutually exclusive
    • Complementary
    • Dependent

15. Events A and B are independent, with P(A) = p and P(B) = q. Which expression gives P(A or B)?

    • pq
    • p + q
    • p + q - 2pq
    • p + q - pq

16. Events A, B and C are mutually independent with P(A) = 0.5, P(B) = 0.4 and P(C) = 0.1. What is the probability that all three occur?

    • 0.001
    • 0.100
    • 0.050
    • 0.020

17. Two fair dice are rolled. Event A is first score even, B is total 7. Are they independent?

    • Yes, independent
    • Cannot be determined
    • No, dependent
    • No, mutually exclusive

18. P(A) = 0.3, P(B) = 0.4 with A and B mutually exclusive. Event C is independent of A with P(C) = 0.5. What is P(A and C)?

    • 0.07
    • 0.00
    • 0.35
    • 0.15

19. A and B are mutually exclusive with P(A) = 0.25 and P(B) = 0.5. What is the probability that neither A nor B occurs?

    • 0.125
    • 0.75
    • 0.25
    • 0.375

20. A and B are independent with P(A) = 0.2 and P(A or B) = 0.44. What is P(B)?

    • 0.40
    • 0.30
    • 0.55
    • 0.24

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