1. (100 points) (This problem is similar to problem 4.0.9 in notes) Youare a lawyer and one of yourclients was hit bya car while crossing the street at a crosswalk. Her injuries required medical treatment andher hospital stay incurred $10 000 in medical expenses. Although the long term prognosis is for a full recoverythere is some chance of permanent damage. Yourclient has been advised bymedical staff if her pain continues to return for furtherexamination.

Just after leaving the hospital your client received an offer from the driver's insurance company for

$120 000 to settle any claims arising from the accident.

Ifsheacceptstheoffershewillreceivethe$120000immediatelyandwillberequiredtosignawayany rightstomoredamagesinthefuture.Ifsherefusestheoffershecansueandtaketheinsurancecompany to trial. Her trial costs will be $15 000. The probability that she will win in court is 85%. If she wins thereisa45%probabilityshewillbeawarded$350000andan55%probabilityshewillbeawarded

$30 000 in damages.

For your initial posting focus on the following questions:

1. Draw the decision tree for the problem as described. What recommendation would you give your client? Should she accept the offer of $120 000 or sue the insurance company in court for thepossibility of a larger settlement? Justify your answer using the decision tree. How if at all would your recommendation change if you allow for the fact that your client is risk averse (that is she prefers lowerrisk)?
2. Consider the same situation as 1) except that there are now twoplayers: you client and the insurancecompany.Theinsurancecompanystartsbydecidinghowlargeasettlementtooffer;

$100 000 $150 000 or $200 000. Youthen decide whether to accept the offer or challenge in court. Usetheideaofzero-sumgametodeterminewhatoffertheinsurancecompanywillmake.Assume the trial costs for the insurance company are $15 000 as well. Justify your answer using a newdecision tree that corresponds to thisproblem.