Question

1. understanding how insurance works

insurance policies are a common form of risk reduction or risk transfer in which a third party assumes some or all of the risks posed by certain dangers. why would the company be willing to assume these risks?
consider a simplified example in which all 30,000 residents in a particular town pay $100 a month to the insurance company securesure for medical insurance coverage. the insurance company cannot predict whether a given resident will need hospitalization or how much any individuals care will cost. suppose, however, it has data that on average, 10% of the citizens require care each month, costing an average of $1,200 each. the expected average cost of monthly care will be $ per person. if the insurance company sets the monthly deductible equal to this amount, it would break even (on average).
in reality, the rates that an individual pays each month vary based on a process known as, in which the insureds are divided into four insurance classes. the class, which is based on an insured persons ines the amount he or she pays.
consider the following example:
an insurance policy in action
carlos is a 21 - year - old college student who recently fell off a roof at a party and had to be the emergency room at a nearby hospital. although an mri revealed that he suffered no internal injuries, and he was released only hours later with mild pain medication, his medical bill for the hospitalization and tests totaled $4,503. carlos is covered under his parents insurance policy, which has a $400 hospital stay deductible and a coinsurance rate of 20%. his parents can therefore expect a reimbursement from the insurance company of $. (note: round your answer to the nearest dollar.)
complete each statement that follows with the appropriate insurance term.

Explanation:

Step1: Calculate expected average cost of monthly care

The formula for expected value is \(E(X)=\sum_{i}x_ip_i\). Here, \(x = 1200\) (cost per person who needs care) and \(p=0.1\) (probability of needing care), and for those who don't need care \(x = 0\) and \(p = 0.9\). But a simpler way is to use the formula based on the group. The total cost for the group is \(0.1\times30000\times1200\). The expected cost per person is \(\frac{0.1\times30000\times1200}{30000}\).

$$
LATEXBLOCK0
$$

Step2: Calculate the reimbursement amount for Carlos

First, subtract the deductible from the total bill: \(4503 - 400=4103\). Then, the insurance company pays \(80\%\) (since the coinsurance rate is \(20\%\)) of the amount after deductible. So the reimbursement amount \(A\) is \(A=(4503 - 400)\times0.8\)

$$
LATEXBLOCK1
$$

Answer:

The expected average cost of monthly care is \(120\) per person. The reimbursement amount is \(3282\)