×
×

# A life insurance company issues standard, preferred, and ISBN: 9780321923271 41

## Solution for problem 6E Chapter 1.5

Probability and Statistical Inference | 9th Edition

• Textbook Solutions
• 2901 Step-by-step solutions solved by professors and subject experts
• Get 24/7 help from StudySoup virtual teaching assistants Probability and Statistical Inference | 9th Edition

4 5 0 342 Reviews
26
5
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(D S) + P(D T) + P(D U)             ………(1)

Where,

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

= 0.6 0.01

= 0.006

Hence, P(D S) = 0.006

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

= 0.3 0.008

= 0.0024

Hence, P(D T) = 0.0024

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

=  0.1 0.007

...

Step 2 of 3

Step 3 of 3

##### 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.

Unlock Textbook Solution