SOLUTION: An insurance company charges $200 for a life insurance premium for people under the age of 18 that pays out $15,000. The probability that someone dies before their 18th birthday is

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Question 138658: An insurance company charges $200 for a life insurance premium for people under the age of 18 that pays out $15,000. The probability that someone dies before their 18th birthday is 0.0025. What is the expected payout by the insurance company? How much of that profit/loss does the company make?
Answer by stanbon(75887) (Show Source):
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An insurance company charges $200 for a life insurance premium for people under the age of 18 that pays out $15,000. The probability that someone dies before their 18th birthday is 0.0025. What is the expected payout by the insurance company? How much of that profit/loss does the company make?
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Let "gain" be the random variable.
Its values are +200 and -15000
Corresponding probabilities are 0.9975 and 0.0025
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E(x) = 200*0.9975 and -15000*0.0025
E(x) = $162
The company can expect to gain $162 during that particular year.
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Cheers,
Stan H.