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It is estimated that there are 22 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.

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Answer:

The insurance company can make $0.78 for each policy that it sells

Step-by-step explanation:

The loss incurred to the insurance company for each death claim is:

[tex]L = \$1-\$100,000=-\$99,999[/tex]

This event has a 22 in 10 million probability of happening.

The gain for the company for each policy not claimed is:

[tex]G= \$1[/tex]

This event has a 9,999,978 in 10 million probability of happening.

The expected value is:

[tex]EV =\$1*\frac{9,999,978}{10,000,000} -\$99,999*\frac{22}{10,000,000} \\EV=\$0.78[/tex]

Therefore, over the long run, the insurance company can make $0.78 for each policy that it sells.

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