3p.08 Know and apply the formal notation for independent events Quiz: Pearson Edexcel Statistics, Unit 3

The 20 questions

1. When are two events defined as independent?

   • Equally likely
   • Mutually exclusive
   • Unchanged probability
   • Exhaustive outcomes

2. Which is the multiplication law for independent events A and B?

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

3. P(A) = 0.5 and P(B) = 0.2, with A and B independent. What is P(A and B)?

   • 0.7
   • 0.1
   • 0.25
   • 0.3

4. For independent events, which statement is true?

   • P(A|B) = P(A)
   • P(A|B) = P(B)
   • P(A|B) = 1
   • P(A|B) = 0

5. Can two mutually exclusive events with non-zero probabilities be independent?

   • Always
   • Sometimes
   • No
   • Yes

6. Which feature describes independent events like repeated coin tosses?

   • Complementary events
   • Always dependent
   • Mutually exclusive
   • Unaffected outcomes

7. P(A) = 0.6 and P(B) = 0.5, with A and B independent. What is P(B | A)?

   • 0.5
   • 0.6
   • 1.1
   • 0.3

8. How do independent events differ from conditional events?

   • Always equal totals
   • No probability change
   • Always mutually exclusive
   • Never share outcomes

9. Two dice are rolled. What is P(both show a six)?

   • 1/12
   • 1/6
   • 2/36
   • 1/36

10. P(A) = 0.3 and P(B) = 0.4, independent. What is P(A and B)?

    • 0.12
    • 0.7
    • 0.07
    • 0.34

11. A machine works with probability 0.9 and two machines are independent. What is P(both work)?

    • 0.81
    • 0.18
    • 1.8
    • 0.9

12. A bag has red counters with probability 0.25 on each draw, with replacement. What is P(red, then red)?

    • 0.125
    • 0.5
    • 0.25
    • 0.0625

13. P(A) = 0.2 and P(B) = 0.6 with A and B independent. What is P(A or B)?

    • 0.4
    • 0.8
    • 0.12
    • 0.68

14. If P(A) = 0.4 and P(A | B) = 0.4, what can be said about A and B?

    • Always conditional
    • They are independent
    • Mutually exclusive
    • Complementary pairs

15. Two spinners are independent. P(spinner 1 shows 3) = 1/4 and P(spinner 2 shows 5) = 1/3. What is P(both)?

    • 1/12
    • 1/7
    • 1/24
    • 7/12

16. Three independent coin flips. What is P(all heads)?

    • 1/3
    • 1/6
    • 1/8
    • 3/8

17. What makes independence impossible for standard mutually exclusive events?

    • Zero intersection
    • Missing denominators
    • Equal probabilities
    • Sum exceeding one

18. If P(A)=0.5, P(B)=0.4 and P(A and B)=0.25, are A and B independent?

    • Cannot tell
    • No
    • Mutually exclusive
    • Yes

19. Which sampling method ensures independent random draws from a bag?

    • With replacement
    • Without replacement
    • Stratified sample
    • Quota sampling

20. What does the formal equation P(A | B) = P(A) indicate?

    • A is a subset
    • Events are independent
    • B has zero chance
    • Events are exclusive

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