P8 calculate the probability of independent and dependent combined events, including... Quiz: Pearson Edexcel Maths, Unit 5

The 20 questions

1. For independent events A and B, what is P(A and B)?

   • P(A) × P(B)
   • P(A) + P(B)
   • P(A) − P(B)
   • P(A) ÷ P(B)

2. What key assumption is needed before multiplying probabilities of two events?

   • Independence
   • Mutual exclusivity
   • Equal weighting
   • Bias correction

3. A fair coin is tossed and a fair die is rolled. What is the probability of heads and a six?

   • 1/12
   • 1/6
   • 1/2
   • 1/3

4. Two fair dice are rolled. What is the probability of two sixes?

   • 1/6
   • 1/12
   • 1/3
   • 1/36

5. A bag has 3 red and 2 blue counters. A counter is picked, replaced, and then picked again. What is P(red then blue)?

   • 1/5
   • 6/25
   • 6/20
   • 3/10

6. A bag has 3 red and 2 blue counters. Without replacement, what is P(red then blue)?

   • 3/20
   • 1/2
   • 3/10
   • 6/25

7. The probability of rain tomorrow is 0.3 and the probability of a late train is 0.2, assuming independence. What is the probability of both?

   • 0.06
   • 0.5
   • 0.1
   • 0.44

8. A fair coin is tossed twice. What is the probability of no heads?

   • 1/2
   • 1/8
   • 1/4
   • 3/4

9. Two independent successes have probabilities 0.9 and 0.8. What is the probability of both?

   • 0.1
   • 0.08
   • 1.7
   • 0.72

10. A pack of 5 cards has 2 aces. Two cards are drawn without replacement. What is P(ace then ace)?

    • 1/5
    • 1/10
    • 4/25
    • 2/5

11. What key assumption is violated if you multiply P(A) by P(B) for linked events?

    • Exhaustiveness
    • Mutually exclusive
    • Complementarity
    • Independence

12. P(A) = 0.4 and P(B given A) = 0.5. What is P(A and B)?

    • 0.9
    • 0.2
    • 0.45
    • 0.1

13. P(A) = 1/3 and P(B) = 1/4 for independent events. What is the probability that neither occurs?

    • 1/12
    • 7/12
    • 5/12
    • 1/2

14. Three draws are made with replacement from a bag with 4 red and 6 blue counters. What is P(all three red)?

    • 0.4
    • 0.12
    • 0.064
    • 0.24

15. Three draws are made without replacement from 10 counters, of which 4 are black. What is P(all three black)?

    • 4/10
    • 1/10
    • 1/30
    • 1/120

16. A fair coin is tossed twice. What is the probability of exactly one head?

    • 1/3
    • 1/4
    • 1/2
    • 3/4

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

    • 0.6
    • 0.1
    • 0.7
    • 0.4

18. A first stage goes to A with probability 0.6 and to B with probability 0.4. From A, yes has probability 0.7; from B, yes has probability 0.2. What is P(yes)?

    • 0.5
    • 0.9
    • 0.42
    • 0.14

19. Two kings are drawn from a standard pack without replacement. What is the probability?

    • 1/221
    • 1/13
    • 1/169
    • 1/663

20. Three independent events have probabilities 0.5, 0.4 and 0.3. What is the probability that all three occur?

    • 0.06
    • 0.12
    • 0.9
    • 0.024

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