# Exam P Practice Problem 39 – Repair Costs for Collision Damage

Problem 39-A

Costs (in thousands) to repair damage to insured cars caused by collisions are independent random variables with common density function:

$\displaystyle f(x)=\frac{1}{50} \ (10-x) \ \ \ \ \ \ \ \ 0

An insurance coverage is available to cover the repair costs subject to a deductible of 2.

Five accidents with collision damages are expected in the comming year. What is the probability that the insurer needs to pay for the repair costs of exactly three of the accidents?

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Problem 39-B

Home owners purchased insurance policies to protect against losses due to fire. The loss amounts (in thousands) are independent and are modeled by the probability distribution with the following density function.

$\displaystyle f(x)=\frac{3}{\text{2000,000}} \ (\text{10,000}-x^2) \ \ \ \ \ \ \ \ 0

Each of these policies has a deductible of 10.

The insurer examines five such losses. What is the probability that the insurer makes payment on more than three of the losses?

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