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For customers purchasing a refrigerator at a certain appliance store, let A be the event that the refrigerator was manufactured in the U.S., B be the event that the refrigerator had an icemaker, and C be the event that the customer purchased an extended warranty. Relevant probabilities are P ( A ) = .75 P ( B | A ) = .9 P ( B | A ′) = .8 P ( C | A ∩ B ) = .8 P ( C | A ∩ B ′) = .6 P ( C | A ′ ∩ B ) = .7 P ( C | A ′ ∩ B ′) = .3 a. Construct a tree diagram consisting of first-, second-, and third-generation branches, and place an event label and appropriate probability next to each branch. b. Compute P ( A ∩ B ∩ C ). c. Compute P ( B ∩ C ). d. Compute P ( C ). e. Compute P ( A | B ∩ C ), the probability of a U.S. purchase given that an icemaker and extended warranty are also purchased.

BuyFind

Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809
BuyFind

Probability and Statistics for Eng...

9th Edition
Jay L. Devore
Publisher: Cengage Learning
ISBN: 9781305251809

Solutions

Chapter
Section
Chapter 2.4, Problem 63E
Textbook Problem

For customers purchasing a refrigerator at a certain appliance store, let A be the event that the refrigerator was manufactured in the U.S., B be the event that the refrigerator had an icemaker, and C be the event that the customer purchased an extended warranty. Relevant probabilities are

P(A) = .75 P(B|A) = .9 P(B|A′) = .8

P(C|AB) = .8 P(C|AB′) = .6

P(C|A′ ∩ B) = .7 P(C|A′ ∩ B′) = .3

  1. a. Construct a tree diagram consisting of first-, second-, and third-generation branches, and place an event label and appropriate probability next to each branch.
  2. b. Compute P(ABC).
  3. c. Compute P(BC).
  4. d. Compute P(C).
  5. e. Compute P(A|BC), the probability of a U.S. purchase given that an icemaker and extended warranty are also purchased.

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Chapter 2 Solutions

Probability and Statistics for Engineering and the Sciences
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