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A store sells four brands of tablets. The least expensive

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Problem 8E Chapter 1.5

Probability and Statistical Inference | 9th Edition

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Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman

Probability and Statistical Inference | 9th Edition

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Problem 8E

PROBLEM 8E

A store sells four brands of tablets. The least expensive brand, B1, accounts for 40% of the sales. The other brands (in order of their price) have the following percentages of sales: B2, 30%; B3, 20%; and B4, 10%. The respective probabilities of needing repair during warranty are 0.10 for B1, 0.05 for B2, 0.03 for B3, and 0.02 for B4. A randomly selected purchaser has a tablet that needs repair under warranty. What are the four conditional probabilities of being brand Bi, i = 1, 2, 3, 4?

Step-by-Step Solution:
Step 1 of 3

Solution 8E

Step1 of 3:

We have,

Probability that the tablets need repair = P(R)

Probability that the least expensive brands are

P() = 40%

            = 0.4

P() = 30%

           = 0.3

P() = 20%

            = 0.2

P() = 10%

           = 0.1

Similarly,

P(R/) = 0.10

P(R/) = 0.05

P(R/) = 0.03

P(R/) = 0.02

We need to find,

What are the four conditional probabilities of being brand Bi, i = 1, 2, 3, 4?

Step2 of 3:

We need to find the Probability that the tablets need repair and it is given by

P(R) = P(R) + P(R) + P(R) + P(R)         ………(1)

Where,

1).P(R) = P()P(R/)                                 [Because P(R/) = ]

                      = 0.40.10

                      = 0.04

     Hence, P(R) = 0.04.

2).P(R) = P()P(R/)                                  [Because P(R/) = ]

                      = 0.30.05

                      = 0.015

     Hence,P(R) = 0.015.

3).P(R) = P()P(R/)                                  [Because P(R/) = ]

                      = 0.20.03

                      = 0.006

     Hence, P(R) = 0.006.

4).P(R) = P()P(R/)                                  [Because P(R/) = ]

 ...

Step 2 of 3

Chapter 1.5, Problem 8E is Solved
Step 3 of 3

Textbook: Probability and Statistical Inference
Edition: 9
Author: Robert V. Hogg, Elliot Tanis, Dale Zimmerman
ISBN: 9780321923271

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A store sells four brands of tablets. The least expensive

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