# Exam P Practice Problem 103 – randomly selected auto collision claims

Problem 103-A

The size of an auto collision claim follows a distribution that has density function $f(x)=2(1-x)$ where $0.

Two randomly selected claims are examined. Compute the probability that one claim is at least twice as large as the other. $\text{ }$ $\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \frac{10}{36}$ $\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \frac{15}{36}$ $\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \frac{20}{36}$ $\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \frac{21}{36}$ $\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \frac{23}{36}$ $\text{ }$ $\text{ }$ $\text{ }$

Problem 103-B

Auto collision claims follow an exponential distribution with mean 2.

For two randomly selected auto collision claims, compute the probability that the larger claim is more than four times the size of the smaller claims. $\text{ }$ $\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ 0.2$ $\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ 0.3$ $\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ 0.4$ $\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ 0.5$ $\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ 0.6$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$ $\text{ }$

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