Question

An auto insurance company insures your car for one year against damage due to collision with another vehicle or object. Your policy has an annual deductible of 400. During the year there is a 90% chance that you will not have a collision and a 10% chance that you will have exactly one collision. Assume that the damage from a collision is approximated by an exponential distribution with mean 1600.

      (a) What is the probability that the insurer will not pay you anything, including the possibility that you don’t have a collision? (Ans 0.92212)

      (b) Given that you have a collision, what is the probability that the insurer won’t pay you more than 600, including the possibility that the damage doesn’t exceed the deductible? (Ans 0.46474)

      (c) Given that you have a collision, determine the expected value of the insurance payment, including     the possibility that the damage doesn’t exceed the deductible. (Ans 1246.08)

      (d) Given that you have damage that exceeds the deductible, what is the probability that the insurer won’t pay you more than 600? (Ans 0.31271)

      (e) Given that you have damage that exceeds the deductible, determine the expected value of the insurance payment. (Ans 1600)

      (f) What is the probability that the insurer won’t pay you more than 600, including the possibility that you don’t have a collision or that you have damage that doesn’t exceed the deductible. SOLVE 2 WAYS, using answers from parts (a) - (e). (Ans 0.94647)

      (g) Determine the expected valued value of the insurance payment, including the possibility that you don’t have a collision or that you have damage that doesn’t exceed the deductible. SOLVE 2 WAYS, using answers from parts (a) - (e). (Ans 124.61)

Answer 1