# Exam P Practice Problem 50 – Payments for Hospitalization

Problem 50-A

An insurer sells a hospital expense plan that pays a fixed sum per day of hospitalization. Suppose that the number of days of hospitalization in a year for someone insured under this plan has the following probability function.

$\displaystyle P(X=x)=\frac{3}{4^{x+1}} \ \ \ \ \ \ \ \ x=0,1,2,3,\cdots$

The plan pays 1,000 for each day of hospitalization up to 4 days a year.

What is the expected payment for hospitalization under this hospital expense plan?

$\displaystyle (A) \ \ \ \ \ \ \ 250.00$

$\displaystyle (B) \ \ \ \ \ \ \ 328.13$

$\displaystyle (C) \ \ \ \ \ \ \ 332.03$

$\displaystyle (D) \ \ \ \ \ \ \ 333.33$

$\displaystyle (E) \ \ \ \ \ \ \ 444.44$

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Problem 50-B

An insurer sells a hospital expense plan that pays cash for each day of hospitalization. Suppose that the number of days of hospitalization in a year for someone insured under this plan has the following probability function.

$\displaystyle P(X=x)=\frac{3}{4^{x+1}} \ \ \ \ \ \ \ \ x=0,1,2,3,\cdots$

The plan pays for each day of hospitalization up to 4 days a year subject to the condition that the plan pays 500 for each of the first 3 days and 2500 for the fourth day.

What is the expected amount paid to the insured under this hospital expense plan?

$\displaystyle (A) \ \ \ \ \ \ \ 150.00$

$\displaystyle (B) \ \ \ \ \ \ \ 166.67$

$\displaystyle (C) \ \ \ \ \ \ \ 169.92$

$\displaystyle (D) \ \ \ \ \ \ \ 173.83$

$\displaystyle (E) \ \ \ \ \ \ \ 175.00$

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