1. After doing some reading on hauntings, you have decided to open a ghost insurance business. Your research shows that a given house has a 1/100 chance of becoming haunted each year (you may assume that multiple hauntings in the same house each year are not possible). You have been assured by a friend that they are able to capture and release ghosts into the wild for a cost of $5000 each haunting. You wish to sell annual ghost insurance policies, and your goal is to make as close as possible to a $100,000 profit each year.

(a) Suppose you charge a yearly premium of P for your ghost insurance. What is your expected value in terms of P for each policy you sell?

(b) Assume you were guaranteed to find N people interested in purchasing ghost insurance. In terms of N, what should their yearly payment be in order for you to expect to meet your profit goals?

(c) Determine the premium you should charge for ghost insurance if you were guaranteed to sell 75 policies. What should the premium be if you were guaranteed to sell 500 policies? What does this tell you about insurance companies in general and the premiums for their customers (assuming the company is just trying to make a fixed dollar amount profit)?

(d) Assume that you are calculating premiums based on your formula in part b). In terms of N, what is the most you could make in a year? What is the least you could make? What are the odds (in terms of N) of each of these scenarios?

(e) Again assuming you are following the premium formula you found in part b), what is the largest number of policies you can sell without having any risk of bankruptcy (i.e. a negative profit for the year)? What should the premium be in this case?