Problem 2 (8 points) Mark Twain is thinking of suing the manufacturer of his car because of a defect that he believes caused him to have an accident and kept him out of work for a year. He is suing the company for $2.6 million. The company has offered him a settlement of $550,000 of which Mark would receive $380,000 after attorney's fees. His attorney has advised him that he has a 45% chance of winning his case. If he loses, he will incur attorneys' fees and court costs of $100,000. If he wins, he is not guaranteed to receive the full $2.6 million. His attorney believes that there is a 40% chance he could receive the full amount, in which case Mark would get $2 million after his attorney takes his cut, and a 60% chance that the jury will award him a lesser amount of $1 million, of which Mark would get halif. Furthermore, in the event of his winning the case or going for the settlement, Mark has to decide at the end of the year as to whether he should invest the money for a year in the stock market or put it into a fixed deposit earning 5% simple interest. If he invests the money in the stock market, he will earn 30% of his investment at the end of the following year under good market condition or lose 20% of his investment under bad market condition. Probabilities to each of the possible market conditions are as follows: Market Conditions Good Bad Probability 0.4 0.6 (a). Should Mark sue the company or take the settlement? Answer this question with a decision tree (b). Based on the decision tree you have, determine the Expected Value of Perfect Information VPI) for conditions of winning or losing the case