Exam P Practice Problem 56 – Reporting of Auto Accidents

Problem 56-A

An insurer sells auto insurance policies that provide collision coverage to drivers. The collision accidents reported by drivers are uniformly distributed across the days of the week.

The day of reporting an accident is independent of the day of reporting of any other accident.

Suppose that in one week, 10 collision accidents are reported to the insurer. What is the probability that more than 3 accidents are reported on Saturday and Sunday?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1269$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.3127$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.4218$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.5782$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.6873$

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Problem 56-B

An insurer sells auto insurance policies that provide collision coverage to drivers. The collision accidents reported by drivers are uniformly distributed across the days of the week.

The day of reporting an accident is independent of the day of reporting of any other accident. The number of accidents reported in one week is also independent of the number of accidents reported in any other week.

Suppose that in one week, 10 collision accidents are reported to the insurer and in the following week, 12 collision accidents are reported to the insurer. What is the probability that more than 20% of the accidents from these two weeks are reported on Saturday and Sunday?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.0571$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.0886$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.2028$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.7972$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.9114$

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