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A life insurance company issues standard, preferred, and

Probability and Statistical Inference | 9th Edition | ISBN: 9780321923271 | Authors: Robert V. Hogg, Elliot Tanis, Dale Zimmerman ISBN: 9780321923271 41

Solution for problem 6E 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 6E

PROBLEM 6E

A life insurance company issues standard, preferred, and ultrapreferred policies. Of the company’s policyholders of a certain age, 60% have standard policies and a probability of 0.01 of dying in the next year, 30% have preferred policies and a probability of 0.008 of dying in the next year, and 10% have ultrapreferred policies and a probability of 0.007 of dying in the next year. A policyholder of that age dies in the next year.What are the conditional probabilities of the deceased having had a standard, a preferred, and an ultrapreferred policy?

Step-by-Step Solution:
Step 1 of 3

Solution 6E

Step1 of 3:

We have,

Standard policy = S

Preferred policy = T

Ultra preferred policy = U

Dies next year = D

We need to find what are the conditional probabilities of the deceased having had a standard, a preferred, and an ultra preferred policy?

Step2 of 3:

From the given information we have,

Probability of Standard policy P(S) = 60%

                                                          = 0.6

Probability of Preferred policy P(T) = 30%

                                                          = 0.3

Probability of Ultra preferred policy P(U) = 10%

                                                                    = 0.1

Similarly,

P(D/S) = 0.01

P(D/T) = 0.008

P(D/U) = 0.007

Now,

We need to find the probability of Dies next year and it is given by

P(D) = P(DS) + P(DT) + P(DU)             ………(1)

Where,

1).P(DS) = P(S)P(D/S)                               [Because P(D/S) = ]

                   = 0.60.01

                   = 0.006

    Hence, P(DS) = 0.006

2).P(DT) = P(T)P(D/T)                              [Because P(D/T) = ]

                   = 0.30.008

                   = 0.0024

     Hence, P(DT) = 0.0024

3).P(DU) =  P(U)P(D/U)                             [Because P(D/U) = ]

                   =  0.10.007

 ...

Step 2 of 3

Chapter 1.5, Problem 6E is Solved
Step 3 of 3

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

This textbook survival guide was created for the textbook: Probability and Statistical Inference , edition: 9. This full solution covers the following key subjects: next, policies, preferred, Probability, standard. This expansive textbook survival guide covers 59 chapters, and 1476 solutions. The answer to “A life insurance company issues standard, preferred, and ultrapreferred policies. Of the company’s policyholders of a certain age, 60% have standard policies and a probability of 0.01 of dying in the next year, 30% have preferred policies and a probability of 0.008 of dying in the next year, and 10% have ultrapreferred policies and a probability of 0.007 of dying in the next year. A policyholder of that age dies in the next year.What are the conditional probabilities of the deceased having had a standard, a preferred, and an ultrapreferred policy?” is broken down into a number of easy to follow steps, and 91 words. Probability and Statistical Inference was written by and is associated to the ISBN: 9780321923271. The full step-by-step solution to problem: 6E from chapter: 1.5 was answered by , our top Statistics solution expert on 07/05/17, 04:50AM. Since the solution to 6E from 1.5 chapter was answered, more than 331 students have viewed the full step-by-step answer.

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