AP Statistics · Topic 4.5

Conditional Probability Practice

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

Practice questions

17

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Sample questions

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  1. Sample 1difficulty 3/5

    A tree diagram shows P(A) = 0.6, P(B|A) = 0.7, P(B|A^c) = 0.2.

    0.6 A 0.4 A^c B 0.7 B^c 0.3 B 0.2 B^c 0.8

    What is P(A and B)?

    • A

      0.70

    • B

      0.60

    • C

      0.30

    • D

      0.42

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    Why

    P(A and B) = P(A) * P(B|A) = 0.6 * 0.7 = 0.42.

  2. Sample 2difficulty 3/5

    A two-way table classifies 100 items by row (X/Y) and column (A/B).

    A B X Y 15 25 35 25

    What is P(A | Y)?

    • A

      35/50

    • B

      15/40

    • C

      35/60

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    • D

      35/100

    Why

    Row Y total = 35 + 25 = 60. P(A | Y) = 35/60.

  3. Sample 3difficulty 3/5

    Definition of conditional probability.

    A B A ∩ B P(A|B) = ?

    P(A | B) equals:

    • A

      P(A) * P(B)

    • B

      P(A and B) / P(B)

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    • C

      P(A) / P(B)

    • D

      P(A) + P(B)

    Why

    By definition, P(A|B) = P(A and B)/P(B).

  4. Sample 4difficulty 3/5

    A bag is chosen at random (50/50). Bag 1: P(Red) = 0.6. Bag 2: P(Red) = 0.3.

    0.5 Bag1 0.5 Bag2 R 0.6 B 0.4 R 0.3 B 0.7

    What is P(Red)?

    • A

      0.60

    • B

      0.45

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    • C

      0.90

    • D

      0.30

    Why

    P(Red) = 0.5(0.6) + 0.5(0.3) = 0.30 + 0.15 = 0.45.

  5. Sample 5difficulty 3/5

    P(A and B) =

    • A

      P(A) · P(B|A)

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    • B

      P(A) + P(B)

    • C

      P(B) − P(A)

    • D

      P(A) · P(B)

    Why

    Holds always (independence is the special case where P(B|A) = P(B)).