# Exam P Practice Problem 72 – Risk Categories of Insured Drivers

Both Problem 72-A and Problem 72-B use the following information.

A large pool of insured drivers consists of three distinct risk categories – low risk drivers, medium risk drivers and high risk drivers. The following table has more information about these insured drivers.

$\displaystyle \begin{bmatrix} \text{Risk}&\text{ }&\text{ }&\text{Percentage} &\text{ }&\text{ }&\text{Probability of} \\\text{Category}&\text{ }&\text{ }&\text{ } &\text{ }&\text{ }&\text{at Least One Collision} \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ \text{Low Risk}&\text{ }&\text{ }&\displaystyle 50 \%&\text{ }&\text{ }&\displaystyle 0.10 \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ \text{Medium Risk}&\text{ }&\text{ }&30 \%&\text{ }&\text{ }&0.20 \\\text{ }&\text{ }&\text{ } &\text{ }&\text{ } \\ \text{High Risk}&\text{ }&\text{ }&20 \%&\text{ }&\text{ }&0.50 \end{bmatrix}$

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Problem 72-A

Three insured drivers are randomly selected from this large pool of insured drivers.

What is the probability that all three insured drivers are drawn from different risk categories?

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.01$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.03$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.06$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.18$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.36$

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Problem 72-B

Four insured drivers are randomly selected from this large pool of insured drivers.

What is the probability that all three risk categories are represented in these four insured drivers?

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.096$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.072$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.108$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.180$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.360$

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$\copyright \ 2013 \ \ \text{Dan Ma}$