# Exam P Practice Problem 60 – Health Insurance Claim Frequency

Problem 60-A

An insurance company issued health insurance policies to individuals. The company determined that $Y$, the number of claims filed by an insured in a year, is a random variable with the following probability function.

$\displaystyle P(Y=y)=0.45 \ (0.55)^{\displaystyle y} \ \ \ \ \ \ y=0,1,2,3,\cdots$

What is the probability that a random selected insured from this group of insured individuals will file more than 5 claims in a year?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.0226$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.0277$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.0357$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.0503$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.0749$

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Problem 60-B

An insurance company issued health insurance policies to individuals. The company determined that $Y$, the number of claims filed by an insured in a year, is a random variable with the following probability function.

$\displaystyle P(Y=y)=0.45 \ (0.55)^{\displaystyle y} \ \ \ \ \ \ y=0,1,2,3,\cdots$

The number of claims filed by one insured individual is independent of the number of claims filed by any other insured individual.

An actuary studied three randomly selected insured individuals from this group of individuals who purchased health policies from this company. What is the probability that these three insured individuals will file more than 6 claims in a year?

$\displaystyle (A) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.0457$

$\displaystyle (B) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.0706$

$\displaystyle (C) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.1495$

$\displaystyle (D) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.2201$

$\displaystyle (E) \ \ \ \ \ \ \ \ \ \ \ \ \ \ 0.2406$

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