# Exam P Practice Problem 51 – Expected Claim Payment

Problem 51-A

The probability that a property will not be damaged in the upcoming year is 0.80. Assume that there is at most one incidence of damage in a year.

When there is a damage to the property, the amount of damage (in thousands) has an exponential distribution with mean 20.

The property owner insured the property against damage by purchasing an insurance policy with a deductible of 5.

What is the probability that the insurer’s payment to the owner will exceed 17.5?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ 0.0649$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ 0.0834$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ 0.3249$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ 0.4169$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ 0.8340$

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Problem 51-B

The probability that a property will not be damaged in the upcoming year is 0.80. Assume that there is at most one incidence of damage in a year.

When there is a damage to the property, the amount of damage (in thousands) has an exponential distribution with mean 20.

The property owner insured the property against damage by purchasing an insurance policy with a deductible of 5.

What is the expected payment made by the insurer to the owner of the property?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ 20.00$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ 4.00$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ 3.89$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ 3.50$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ 3.12$

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