You can insure a $35,000diamond for its total value by paying a premium ofDdollars.If the probability of loss in a given year is estimated to be 0.01, what premium should the insurance company charge if it wants the expected gain to equal $1,000?

Step 1

LetGbe the total gain to the insurance company. If the insurance company does not have to pay for the loss of the diamond, then the gain to the insurance company is the amount of the premium,Ddollars. If the insurance company does have to pay for the loss of the diamond, they must pay $35,000. However, the insurance company already receivedDdollars, so the amount of money they will actually gain after receivingDdollars and paying out $35,000is given by the expression $ (D-35000)

The probability of loss in a given year is estimated to be 0.01, so the probability there is not a loss in a given year is 10.01 = 0.99.

Thus, we have the following probability distribution for the gain,G, in dollars.

Fill the table below

G	p(G)
D	?
?	?