A potential customer for an $85,000 fire insurance policy possesses a home in an area that, according to experience, may sustain a total loss in a given year with probability of .001 and a 50% loss with probability .01. Ignoring all other partial losses, what premium should the insurance company charge for a yearly policy in order to break even on all $85,000 policies in this area?

Answer:$510Step-by-step explanation:Let X be the amount of money that insurance company will have to pay on the policy for home.It is given that according to experience, may sustain a total loss in a given year with probability of .001 and a 50% loss with probability .01. Ignoring all other partial losses.It means the possible values for variable X are 0, 42500 and 85000.[tex]P(X=42500)=0.01[/tex][tex]P(X=85000)=0.001[/tex]We have only three possible values of X. So,[tex]P(X=0)+P(X=42500)+P(X=85000)=1[/tex][tex]P(X=0)=1-0.01-0.001=0.989[/tex]The expected amount of money is[tex]E(X)=\sum xP(x)[/tex][tex]E(X)=0\cdot P(X=0)+42500\cdot P(X=42500)+85000\cdot P(X=85000)[/tex][tex]E(X)=0\cdot (0.989)+42500\cdot (0.01)+85000\cdot (0.001)[/tex][tex]E(X)=0+425+85[/tex][tex]E(X)=510[/tex]Therefore, the insurance company should charge a premium of $510 for a yearly policy in order to break even on all $85,000 policies in this area.