Option 1.  A law firm has been offered a chance to settle a case for $30,000 (their client would pay the $30,000, plus a $2,000 fee to the law firm.  

Option 2.  is to immediately go to court.  If they go to court, there would be a 20% chance that they win the case, and hence an 80% chance of losing the case.  If they lose the case, they feel that there is a 70% chance of a $10,000 settlement against their client, and their client will not appeal this. In addition to the $10,000 settlement, the client would pay $3,000 in legal fees. However, there is a 30% chance that the settlement against their client would be set at $100,000.  This they would appeal, and they estimate a 40% chance of winning the appeal and having no settlement against their client, except for the $15,000 legal cost of the appeal.  This means there is a 60% chance of losing the appeal, and the client would end up having to pay the original $100,000 settlement plus the $15,000 cost of the appeal.  

Option 3.  is to make a counter offer of $20,000; there is a 40% chance it would be accepted.  If it is not accepted they could decide to turn the case over to arbitration or go to trial.  They believe there is a chance the arbitrator finds against their client: 

 30% chance client pays $10,000

40% client pays $5,000 

10% chance client pays $100,000 

20% chance client pays nothing.

 The arbitrator charges $3,000.  If they go to trial and lose, they will not appeal.  They believe there would be a 70% chance of losing the case and paying $50,000 and a 30% chance of winning and only incurring $10,000 in legal fees.  If they lose the case they also incur the $10,000 legal expenses.

 A. Draw the Decision Tree for this problem. 

 B. By hand, using the criteria of minimizing the expected cost, determine the optimal strategy for your client.  Show all your work. Be sure to Draw out the Final Strategy.

 C. By hand, create a risk analysis of your strategy in question "b"