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A private pilot wishes to insure his airplane for ​$. The insurance company estimates that a total loss will occur with probability ​, a ​% loss with probability ​, and a ​% loss with probability. Ignoring all other partial​ losses, what premium should the insurance company charge each year to realize an average profit of ​$​?.

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The premium that the insurance company should charge each year to realize an average profit of ​$​500 is $6,900.

First step is to calculated the expected amount to pay

Expected amount=Total loss  +50% loss+25% loss

Expected amount=$200,000(0.002)(1)+$200,000(0.01)(0.5)+$200,000(0.1)(0.25)

Expected amount=$400+$1,000+$5,000

Expected amount=$6,400

Second step is to calculate the premium

Premium=Expected amount+ Average profit

Premium=$6,400+$500

Premium=$6,900

Inconclusion the premium that the insurance company should charge each year to realize an average profit of ​$​500 is $6,900.

Learn more about insurance premium here:https://brainly.com/question/24441770

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