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In probability theory, the expected value of a random variable is the weighted average of all possible values that the random variable can take on. Health insurance companies sell health insurance with an objective to make a profit. The expected value of the net amount paid out by the company in this case is positive for an ailing policy holder and negative for a healthy policy holder.
When the insurance policy is being designed the amount payable if the person falls ill and the premium that is to be paid to the insurance company is fixed such that the expected value of the net amount that the company has to pay if all policy holders are considered is negative.
As an illustration, if a health insurance is being sold to 100 people and there is a probability of 2% percent that any person falls ill and can claim $5000, the premium for the policy would have to be higher than (2*5000)/100 = $100. The expected value of what the company pays is positive for the 2% that fall ill but negative for the other 98%. Overall, the company would have to pay out $10000 but receives more than $10000 as premium. The difference is the company's profit.
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