$1.$ 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 $90,000$ residents in a particular town pay $$100$ a month to the insurance company SecureSure for medical insurance coverage. The insurance company cannot predict whether a given resident will need hospitalization or how much any individual$$s care will cost. Suppose, however, it has data that on average, $10\%$ of the citizens require care each month, costing an average of $$1,000$ each. The expected average cost of monthly care will be $

per person. If the insurance company sets the monthly 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 person$$s $,$ determines the amount he or she pays.

Consider the following example:

An Insurance Policy in Action

Dmitri is a $65-$year$-$old man who recently experienced what he thought were stroke$-$like symptoms and went to the emergency room at a nearby hospital. Although it turned out to be a severe case of heartburn, not a stroke, his medical bill for the hospitalization and tests totaled $$4,946.$ Dmitri has an insurance policy with a $$500$ hospital stay deductible and a coinsurance rate of $20\%.$ He 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.

$$ Dmitri$$s age and history of heart attacks increase his chances of suffering an insurable loss. This is an example of $.$

$$ It is easier for the insurance company to predict the risk associated with an entire town than to predict the risks of a given individual. This reflects the $.$

$$ Because Dmitri is older and has a history of heart attacks, he is a part of the class of insured.