3p.09 Know and apply the formal notation for conditional probability Quiz: Pearson Edexcel Statistics, Unit 3

The 20 questions

1. In probability notation, what does P(B | A) represent?

   • Probability of A
   • Mutually exclusive sum
   • Probability given A
   • Combined intersection

2. Which is the formula for conditional probability?

   • P(B | A) = P(A or B) / P(B)
   • P(B | A) = P(A) x P(B)
   • P(B | A) = P(A) / P(A and B)
   • P(B | A) = P(A and B) / P(A)

3. P(A and B) = 0.12 and P(A) = 0.4. What is P(B | A)?

   • 0.48
   • 0.033
   • 0.3
   • 0.52

4. In the conditional probability expression P(A | B), what does B represent?

   • Sample space total
   • Target outcome
   • Complementary event
   • Given information

5. P(A) = 0.5 and P(B | A) = 0.2. What is P(A and B)?

   • 0.7
   • 0.4
   • 2.5
   • 0.1

6. Is conditional probability P(B | A) always equal to P(A | B)?

   • Only for independent events
   • No
   • Always yes
   • Only when mutually exclusive

7. What does calculating a conditional probability restrict?

   • The theoretical model
   • The sample space
   • The number of trials
   • The mean value

8. Which tool helps find conditional probabilities from data?

   • A scatter diagram
   • A two-way table
   • A pie chart only
   • A histogram of ages

9. 60 students: 36 play sport. Of the sport players, 20 are girls. What is P(girl | plays sport)?

   • 1/3
   • 5/9
   • 2/3
   • 1/2

10. P(A) = 0.25 and P(A and B) = 0.05. What is P(B | A)?

    • 0.3
    • 1.25
    • 0.05
    • 0.2

11. A bag has 4 red and 6 blue counters. Two are drawn without replacement. What is P(second red | first red)?

    • 4/10
    • 1/2
    • 3/10
    • 1/3

12. P(cloudy) = 0.4 and P(rain | cloudy) = 0.6. What is P(cloudy and rain)?

    • 0.6
    • 0.24
    • 0.15
    • 1.0

13. A table shows 25 people in group Y and 15 of them have pets. What is P(pet | Y)?

    • 0.4
    • 0.25
    • 0.15
    • 0.6

14. P(B) = 0.3 and P(A | B) = 0.5. What is P(A and B)?

    • 0.6
    • 0.15
    • 0.35
    • 0.8

15. On a tree diagram, P(first red) = 0.5, P(second red | first red) = 0.4 and P(second red | first not red) = 0.6. What is P(second red | first red)?

    • 0.2
    • 0.6
    • 0.5
    • 0.4

16. 30 windy days are recorded and 12 of them are rainy. What is P(rain | windy)?

    • 0.3
    • 0.4
    • 0.12
    • 2.5

17. Given P(A) = 0.2 and P(B | A) = 0.6, what is P(A and B)?

    • 0.4
    • 0.03
    • 0.8
    • 0.12

18. Why can P(A | B) differ from P(B | A)?

    • Different given events
    • Equal numerators
    • Same denominators
    • Mutually exclusive

19. P(A) = 0.4, P(B) = 0.25 and P(A and B) = 0.1. What is P(B | A)?

    • 0.1
    • 0.4
    • 0.25
    • 0.15

20. What does the denominator represent in a conditional probability formula?

    • Union
    • Total space
    • Intersection
    • Given event

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