AP Statistics · Topic 4.6

Independent Events and Unions of Events Practice

Part of Probability, Random Variables, and Probability Distributions.(VAR-4.D)

Practice questions

10

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Sample questions

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  1. Sample 1difficulty 3/5

    Two independent events have P(A) = 0.7, P(B) = 0.6.

    A: 0.7 B: 0.6 independent

    What is P(A or B)?

    • A

      0.30

    • B

      0.88

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    • C

      1.30

    • D

      0.42

    Why

    P(A and B) = 0.42. P(A or B) = 0.7 + 0.6 - 0.42 = 0.88.

  2. Sample 2difficulty 3/5

    A bag contains 5 red and 3 blue marbles. Two are drawn without replacement.

    5 Red, 3 Blue

    What is the probability both are red?

    • A

      20/56

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    • B

      10/28

    • C

      5/8

    • D

      25/64

    Why

    P(R1) * P(R2|R1) = (5/8) * (4/7) = 20/56.

  3. Sample 3difficulty 3/5

    A two-way table of 100 outcomes is shown.

    A A^c B B^c 12 18 28 42

    Are events A and B independent?

    • A

      No; P(A|B) ≠ P(A)

    • B

      Cannot determine

    • C

      Yes; P(A|B) = P(A) = 0.40

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    • D

      Yes; they are mutually exclusive

    Why

    P(A) = 40/100 = 0.40. P(A|B) = 12/30 = 0.40. Since equal, A and B are independent.

  4. Sample 4difficulty 3/5

    Three independent events each have probability 0.4.

    0.4 S 0.6 F SSS 3 independent trials

    What is the probability all three occur?

    • A

      0.160

    • B

      1.200

    • C

      0.400

    • D

      0.064

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    Why

    Independence: 0.4^3 = 0.064.

  5. Sample 5difficulty 3/5

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

    • A

      0.90

    • B

      0.20

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    • C

      0.50

    • D

      0.10

    Why

    0.5 × 0.4 = 0.20.