Please answer this in 10 minutes

1. (12 points) A Pittsburgh based insurance company estimates that a failure of the battery on an electric car will occur within five years with a probability of 0.02. They write a policy to an electric car owner to the effect that if the car battery fails within five years, a compensation of $20,000 must be paid to the car owner. In the meantime, the insurance company charges the car owner a lump-sum premium of r (charged once in five years), regardless of whether the battery fails or not. The company's profit equals the premium they receive minus the compensation they make to the car owner (if any). (a) If the premium r = $300, what is the expected value of the company's profit? (b) What is the lowest premium value r the company should charge to make sure that the expected value of their profit is non-negative