P4 apply the property that the probabilities of an exhaustive set of outcomes sum to one Quiz: Pearson Edexcel Maths, Unit 5

The 20 questions

1. What do the probabilities of an exhaustive set of outcomes always sum to?

   • 0
   • 0.5
   • 100
   • 1

2. A spinner has P(red) = 0.3 and P(blue) = 0.45, and P(green) = x. What is x?

   • 1.25
   • 0.75
   • 0.25
   • 0.15

3. Outcomes A, B, C and D have probabilities 1/4, 1/3 and 1/6 for A, B and C. What is P(D)?

   • 1/4
   • 1/2
   • 3/4
   • 1/12

4. The probability of no rain is 0.72. What is the probability of rain?

   • 0.28
   • 0.36
   • 0.72
   • 1.72

5. If outcomes have probabilities 0.2, 0.5 and 0.3, what do they show?

   • Mutually exclusive
   • Exhaustive set
   • Biased trials
   • Impossible events

6. A biased die has probabilities 0.1, 0.15, 0.2, 0.25 and 0.1 for 1 to 5. What is P(6)?

   • 0.2
   • 0.25
   • 0.3
   • 0.1

7. Events A and B are mutually exclusive with P(A) = 0.45 and P(B) = 0.3. What is P(A or B)?

   • 1.35
   • 0.135
   • 0.75
   • 0.15

8. Outcomes have probabilities 5x, 3x and 2x and together they are exhaustive. What is the probability of the first outcome?

   • 0.2
   • 0.5
   • 0.3
   • 0.1

9. Which of these forms an exhaustive set of outcomes for a single coin toss?

   • Two heads
   • Tails and edge
   • Heads only
   • Heads and tails

10. A day is sunny with probability 0.4, cloudy with probability 0.35 and rainy with probability 0.25. What is P(not sunny)?

    • 0.65
    • 0.4
    • 0.75
    • 0.6

11. A survey gives P(bus) = 0.35, P(car) = 0.4 and P(other) = 0.1. What is P(walk)?

    • 0.25
    • 0.15
    • 0.05
    • 0.5

12. A player wins with probability 0.6 and draws with probability 0.15. What is the probability of losing?

    • 0.75
    • 0.25
    • 0.15
    • 0.4

13. Two exhaustive outcomes have probabilities in the ratio 1 : 4. What is the probability of the smaller outcome?

    • 0.4
    • 0.2
    • 0.8
    • 0.25

14. A game has P(win) = x, P(lose) = 2x and P(draw) = 0.1. What is x?

    • 0.45
    • 0.2
    • 0.9
    • 0.3

15. Events A and B are mutually exclusive. P(A) = 0.3 and P(neither A nor B) = 0.5. What is P(B)?

    • 0.8
    • 0.15
    • 0.2
    • 0.5

16. A spinner has P(A) = 3/8 and P(B) = 1/4. What is the probability of C or D together?

    • 1/8
    • 5/8
    • 3/8
    • 1/4

17. A fair die is rolled. What is the probability that the score is odd or even?

    • 0.5
    • 0
    • 1
    • 3

18. What is the key feature of mutually exclusive events?

    • Cannot both occur
    • Must sum to 1
    • Always equal
    • Dependent outcomes

19. Four outcomes have probabilities proportional to 1, 2, 3 and 4. What is the probability of the outcome with weight 3?

    • 0.4
    • 0.3
    • 0.25
    • 0.1

20. Can events A and B be mutually exclusive if P(A) = 0.6 and P(B) = 0.5?

    • Yes
    • Always
    • No
    • Maybe

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