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Conditional probability and independence

10th grade (Year 11 in England) · 16 questions · Common Core: HSS.CP.A.3, HSS.CP.A.4, HSS.CP.B.6 · England: GCSE Higher Probability

Name

Date

Score/ 16

  1. Question 1

    P(A) = 0.2, P(B) = 0.5 and P(A and B) = 0.2. Are A and B independent?

    • A. Yes
    • B. No

  2. Question 2

    Survey: Likes science & is in Club — 14; Likes science & not in Club — 16; Doesn't like science & in Club — 16; neither — 18. Given a student is in the Club, what is the probability they like science? Simplest form.

    Answer(as a fraction)

  3. Question 3

    P(A) = 0.6, P(B) = 0.25 and P(A and B) = 0.15. Are A and B independent?

    • A. Yes
    • B. No

  4. Question 4

    Survey: Likes science & is in Club — 12; Likes science & not in Club — 21; Doesn't like science & in Club — 7; neither — 16. Given a student is in the Club, what is the probability they like science? Simplest form.

    Answer(as a fraction)

  5. Question 5

    P(A) = 0.6, P(B) = 0.5 and P(A and B) = 0.4. Are A and B independent?

    • A. Yes
    • B. No

  6. Question 6

    Survey: Likes science & is in Club — 16; Likes science & not in Club — 24; Doesn't like science & in Club — 13; neither — 5. Given a student is in the Club, what is the probability they like science? Simplest form.

    Answer(as a fraction)

  7. Question 7

    P(A) = 0.5, P(B) = 0.4 and P(A and B) = 0.2. Are A and B independent?

    • A. Yes
    • B. No

  8. Question 8

    Survey: Likes science & is in Club — 22; Likes science & not in Club — 16; Doesn't like science & in Club — 14; neither — 23. Given a student is in the Club, what is the probability they like science? Simplest form.

    Answer(as a fraction)

  9. Question 9

    P(A) = 0.4, P(B) = 0.25 and P(A and B) = 0.1. Are A and B independent?

    • A. Yes
    • B. No

  10. Question 10

    Survey: Likes science & is in Club — 15; Likes science & not in Club — 15; Doesn't like science & in Club — 14; neither — 24. Given a student is in the Club, what is the probability they like science? Simplest form.

    Answer(as a fraction)

  11. Question 11

    P(A) = 0.4, P(B) = 0.5 and P(A and B) = 0.16. Are A and B independent?

    • A. Yes
    • B. No

  12. Question 12

    Survey: Likes science & is in Club — 19; Likes science & not in Club — 15; Doesn't like science & in Club — 6; neither — 14. Given a student is in the Club, what is the probability they like science? Simplest form.

    Answer(as a fraction)

  13. Question 13

    P(A) = 0.2, P(B) = 0.2 and P(A and B) = 0.04. Are A and B independent?

    • A. Yes
    • B. No

  14. Question 14

    Survey: Likes science & is in Club — 18; Likes science & not in Club — 16; Doesn't like science & in Club — 24; neither — 6. Given a student is in the Club, what is the probability they like science? Simplest form.

    Answer(as a fraction)

  15. Question 15

    P(A) = 0.3, P(B) = 0.2 and P(A and B) = 0.02. Are A and B independent?

    • A. Yes
    • B. No

  16. Question 16

    Survey: Likes science & is in Club — 14; Likes science & not in Club — 17; Doesn't like science & in Club — 6; neither — 23. Given a student is in the Club, what is the probability they like science? Simplest form.

    Answer(as a fraction)

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Answer key: Conditional probability and independence

  1. 1. B. No

  2. 2. 7/15

  3. 3. A. Yes

  4. 4. 12/19

  5. 5. B. No

  6. 6. 16/29

  7. 7. A. Yes

  8. 8. 11/18

  9. 9. A. Yes

  10. 10. 15/29

  11. 11. B. No

  12. 12. 19/25

  13. 13. A. Yes

  14. 14. 3/7

  15. 15. B. No

  16. 16. 7/10