2.03d The concept of conditional probability Quiz: OCR Maths, Unit 13

The 20 questions

1. Which formula correctly calculates the conditional probability P(A|B)?

   • P(A) / P(B)
   • P(A ∩ B) / P(A)
   • P(A ∩ B) / P(B)
   • P(A ∪ B) / P(B)

2. How is the multiplication rule P(A ∩ B) expressed using conditional probability?

   • P(A) + P(B|A)
   • P(A) / P(B|A)
   • P(A) × P(A|B)
   • P(A) × P(B|A)

3. Which formula correctly calculates the probability of event A or event B occurring?

   • P(A) + P(B) - P(A ∩ B)
   • P(A) + P(B)
   • P(A) + P(B) + P(A ∩ B)
   • P(A) × P(B) - P(A ∩ B)

4. If events A and B are independent, what is P(A|B) equal to?

   • P(A)
   • P(B)
   • 0
   • P(A ∩ B)

5. In the probability notation P(A|B), what does the vertical bar symbol mean?

   • Divided by
   • Given that
   • Intersecting with
   • Union with

6. If events A and B are mutually exclusive with P(B) > 0, what is P(A|B)?

   • P(A)
   • 0
   • P(B)
   • 1

7. What must the sum of all probabilities in a discrete probability distribution equal?

   • 0.5
   • 0
   • 1
   • 100

8. What does conditional probability measure given prior information?

   • Probability
   • Expectation
   • Variance
   • Mean

9. Given that P(A ∩ B) = 0.2 and P(B) = 0.5, what is P(A|B)?

   • 0.25
   • 0.7
   • 0.4
   • 0.1

10. Given P(A) = 0.6 and P(B|A) = 0.3, what is P(A ∩ B)?

    • 0.18
    • 0.2
    • 0.5
    • 0.9

11. Given P(A) = 0.4, P(B) = 0.5, and P(A ∩ B) = 0.1, find P(A ∪ B).

    • 0.7
    • 0.8
    • 0.2
    • 0.9

12. Given P(A) = 0.5, P(B) = 0.4, and P(A ∪ B) = 0.7, find P(A ∩ B).

    • 0.3
    • 0.1
    • 0.6
    • 0.2

13. A bag has 3 red and 7 blue balls. Two are drawn without replacement. Find P(Second Red | First Red).

    • 3/10
    • 3/9
    • 2/10
    • 2/9

14. A fair die shows 5. What is the conditional probability that the sum of two fair dice is 8?

    • 1/6
    • 5/36
    • 1/18
    • 1/36

15. When modelling daily weather, which assumption is often unrealistic?

    • Constant sample space
    • Equal event probabilities
    • Mutually exclusive outcomes
    • Independence of events

16. If P(B) = 0.8 and P(A ∩ B) = 0.6, what is the value of P(A|B)?

    • 0.2
    • 0.48
    • 1.33
    • 0.75

17. Given P(A) = 0.5, P(B) = 0.6, and P(A ∪ B) = 0.8, calculate P(A|B).

    • 0.3
    • 0.5
    • 0.6
    • 0.375

18. If P(A|B) = 0.4 and P(B) = 0.5, what is the value of P(A' ∩ B)?

    • 0.6
    • 0.3
    • 0.1
    • 0.2

19. If event A is a subset of event B and P(A) > 0, what is P(B|A)?

    • P(A)
    • 1
    • P(B)
    • 0

20. If events A and B are independent, P(A) = 0.5 and P(B) = 0.2, what is P(A|B')?

    • 0.5
    • 0.625
    • 0.4
    • 0.1

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