You are considering the possibility of insuring the contents of your home against theft for a period of one year. You estimate the contents of your home at $ 20,000. According to City of Ottawa statistics, there is a 3% chance that your home will be the target of burglars. In the event of a burglary, your losses would be estimated at 10%, 20%, or 40% of the contents with respective probabilities of 50%, 35% and 15%. (Burglars do not steal the entire contents of your residence, as they are looking for items that they can easily pick up and they only have a limited time.) An insurance policy from General Accident Inc. (AG) costs $ 200 / year and guaranteed to replace 100% of loss due to theft. A Federation des Assureurs (FA) insurance policy is less expensive and costs $ 100 / year, but you have to pay a deductible of $ X of all losses (for example, if X = 200, then you pay the first $ 200). An insurance policy from Prudential Assurances (PA) is even cheaper at $ 75 / year, but it only replaces a fraction of Y% losses. Of course, you could also choose not to insure your home. Suppose there can only be one break-in per year at most.

Ex2_Q1. What should you do if X = 300 and Y = 80% knowing that your goal is to minimize your losses for the year? Find the solution by drawing a decision tree.