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?

\text{ }

      \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?

\text{ }

      \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}

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