Exam P Practice Problem 78 – Tracking A Group of Insureds

Problem 78-A

An insurance company tracked a group of 625 insureds for 2 years. It was found that 370 of the insureds had no claims in year 1 and 395 of the insureds had no claims in year 2. Furthermore, there were five times as many insureds who had no claims in both years than there were insureds who had claims in both years.

Select an insured at random from this group. What is the probability that the randomly selected insured had no claims in both years?

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.23$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.28$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.34$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.44$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.47$

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Problem 78-B

An insurance company tracked a group of 1000 insureds for 2 years. It was found that 550 of the insureds had no claims in year 1 and 680 of the insureds had at least one claim in year 2. Of the insureds who had at least one claim in year 1, 306 insureds had at least one claim in year 2.

Select an insured at random from this group. Given that this insured had no claims in year 1, what is the probability that the selected insured had no claims in year 2?

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$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.176$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.230$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.320$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.418$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.764$

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