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The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance is as follows. Payment ($) Probability 0.85 500 0.04 1,000 0.04 3,000 0.03 5,000 0.02 8,000 0.01 10,000 0.01 a Use the expected collision payment to determine the collision insurance premium that would enable the company to break even. b. The insurance company charges an annual rate of $520 for the collision coverage. What is the expected value of the collision policy for a policyholder? (Hint: It is the expected payments from the company minus the cost of coverage.) Why does the policyholder purchase a collision policy with this expected value?

The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance is as follows. Payment ($) Probability 0.85 500 0.04 1,000 0.04 3,000 0.03 5,000 0.02 8,000 0.01 10,000 0.01 a Use the expected collision payment to determine the collision insurance premium that would enable the company to break even. b. The insurance company charges an annual rate of $520 for the collision coverage. What is the expected value of the collision policy for a policyholder? (Hint: It is the expected payments from the company minus the cost of coverage.) Why does the policyholder purchase a collision policy with this expected value?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance is as follows: | Payment ($) | Probability | |-------------|-------------| | 0 | 0.85 | | 500 | 0.04 | | 1,000 | 0.04 | | 3,000 | 0.03 | | 5,000 | 0.02 | | 8,000 | 0.01 | | 10,000 | 0.01 | ### Tasks a. Use the expected collision payment to determine the collision insurance premium that would enable the company to break even. b. The insurance company charges an annual rate of $520 for the collision coverage. What is the expected value of the collision policy for a policyholder? *(Hint: It is the expected payments from the company minus the cost of coverage.)* Why does the policyholder purchase a collision policy with this expected value?
Transcribed Image Text:The probability distribution for damage claims paid by the Newton Automobile Insurance Company on collision insurance is as follows: | Payment ($) | Probability | |-------------|-------------| | 0 | 0.85 | | 500 | 0.04 | | 1,000 | 0.04 | | 3,000 | 0.03 | | 5,000 | 0.02 | | 8,000 | 0.01 | | 10,000 | 0.01 | ### Tasks a. Use the expected collision payment to determine the collision insurance premium that would enable the company to break even. b. The insurance company charges an annual rate of $520 for the collision coverage. What is the expected value of the collision policy for a policyholder? *(Hint: It is the expected payments from the company minus the cost of coverage.)* Why does the policyholder purchase a collision policy with this expected value?
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