Please provide steps and explanations. Thank you. A private pilot wishes to insu

Question

Please provide steps and explanations. Thank you.

A private pilot wishes to insure his airplane for $500,000. The insurance company estimates that a total loss will occur with probability 0.003, a 50% loss with probability 0.04, and a 25% loss with probability 0.2. Ignoring all other partial losses, what premium should the insurance company charge each year to realize an average profit of $1000? The insurance company should charge s each year. (Type an integer or a decimal. Round to the nearest dollar as needed.)

Explanation / Answer

Soln,

We can start by calculating the expected value that how much the client or the pilot has to pay as premium, so break it in 3 parts .

Case 1 If the total loss will happen the compay will have to pay complete amount that is $500,000 having probaility 0.003.

Case 2, If 50% loss have to pay that means Company will have to pay $ 500,000 * 0.5 with probability of 0.04.

Case 3, if 25 % Loss have to be paid by company then Company will pay $500,000 *0.25 with probaibility 0.2.

So the expected value we can write as

E(X)= $500.000*(1*0.003+0.5*0.04+0.25*0.2)

so, E(X) = $ 36,500.

Since the Insurance company wishs a $1000 more as profit so They will charge the pilot $37,500 as premium.

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