Please answer all questions with full and clear solution steps.

Q3: Julia Cho, an attorney for North Hope Hospital (NHH), is in a bad mood today. She's just learned that a malpractice lawsuit against one of the hospital's surgeons is being allowed to proceed. In cases like this, NHH always attempts to settle, meaning Julia will offer the patient a sum of money and hope that they accept, which would bring an end to the situation. Julia is considering two options: she could either offer a small settlement ($30K) or a large one ($180K). Obviously, patients are more likely to accept a larger offer: historically, about 85% of patients have accepted offers of $180K, while only about 50% of patients have accepted offers of $30K. If the patient rejects the settlement offer, then the case will denitely proceed to trial. Fortunately, Julia is quite condent that NHH would win in court: she estimates there's only a 20% chance of losing the trial, which is good, because the payouts are typically steep. If the patient wins in court, Julia estimates NHH would have to pay the patient about $400K in fees. If NHH wins in court, there is no prot or loss for NHH (the salaries of NHH's in-house legal team are not considered part of the fees associated with a trial). So...what to do? a. Construct a decision tree that models Julia's situation, including all events, decisions, probabilities, and payoff values. (3 points) b. Using the risk neutral (EMV) approach, solve for Julia's optimal decision strategy and provide a brief (2-3 sentences) recommendation to Julia. (2 points)