Let X be the damage incurred (in $) in a certain type of accident during a given year. Possible X values are 0, 1000, 5000, and 10000, with probabilities .8, .1, .08, and .02, respectively. A particular company offers a $500 deductible policy. If the company wishes its expected profit to be $100, what premium amount should it charge?

Answer Step 1 of 3 Let x=The damage incurred y=premium should charge g=The cost to insurance company Then g(x)=x-500 y(x)=E(g(x))+100 P(x)= probability assigned Step 2 of 3 x P(x) g(x)=x-500 y(x) 0 0.8 0 100 1000 0.1 500 600 5000 0.08 4500 4600 10000 0.02 9500 9600