SOLUTION: It is estimated that there are 16 deaths for every 10 million people who use airplanes. A company that sells flight insurance provides​ $100,000 in case of death in a plane

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Question 1076635: It is estimated that there are 16 deaths for every 10 million people who use airplanes. A company that sells flight insurance provides​ $100,000 in case of death in a plane crash. A policy can be purchased for​ $1. Calculate the expected value and thereby determine how much the insurance company can make over the long run for each policy that it sells.
The expected value is ​$
Answer by Theo(13342)   (Show Source): You can put this solution on YOUR website!
the probability of dying in an airplane is equal to 16 / 10,000,000.

the insurance company gets 1 dollar from every person who buys the insurance policy.

if a person dies in an airplane crash, that person's beneficiary gets $100,000.

the expected value to the insurance company for every insurance policy sold is 1 - 16/10,000,000 * 100,000

using scientific notation, this is equal to 1 - 16/10^6 * 10^4.

simplify to get 1 - 16/10^2 which is equal to 1 - 16/100 which is equal to 1 - .16 which is equal to .84

for every insurance policy sold, the expected value is 84 cents.

for example, assume 10,000,000 people bought the insurance policy.

the company gets 10,000,000 in revenue.

16 of those people die in a plane crash, so the company pays out 16 * 100,000 = 1,600,000 dollars.

the company's gross profit is 10,000,000 - 1,600,000 = 8,400,000 dollars.

divide 8,400,000 by 10,000,000 and you get an average gross profit of .84 for every insurance policy sold.









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