David is a film producer and he is currently evaluating a new horror movie script. David estimates that the probability of a new movie being a success is 0.10 and the probability that it will fail at the box office is 0.90. The studios accounting department estimates that if this new movie is a hit, it will make $25 million in profit, whereas if it fails, it will lose $8 million.

David would also like to consider the service of a noted film critic, Alison, and ask her to assess the movies chance of success. Alison is able to correctly predict a successful film 70% of the time. She is also able to correctly predict an unsuccessful film 80% of the time.

1. Use the likelihoods/conditional and prior probabilities, and calculate all the revised probabilities. Show your work/calculations. (6 points)

2. Draw a decision tree for this problem to help David make the best decision. Solve the decision tree and determine the decision strategy David should follow and its expected profit. (Show your work/calculations). Verbally communicate the decision strategy (20 points)

3. What is the expected value of sample information provided by Alison (EVSI)? Show your work/calculations. Verbally communicate the result. (3 points)

4. Calculate the expected value of perfect information (EVPI) and find out the efficiency of the information provided by Alison. Show your work/calculations. (6 points)