Film producer,JackMagnet,is evaluating a script for a potential film. Based on that script,Magnethas initially estimated the probability of the film being a hit at 0.05, average at 0.1,andtheprobability of it being a flop 0.85. The studio accounting department estimates that if it is a hit, the film will make $320 million in profit,with an average take profits are estimated to be $90 million,andif a flop, will lose $50 million.

Prior to deciding whether or not to produce a film,Magnetcantodecide whether or not to hirea prominentfilm critic toreview andevaluate the script. A large number ofcritic's previous reviews/assessments are available, as well as the final outcome of the associated productions. Using this information, we can calculate that, given a positive review, the probability of a hit would increase to 0.12,the probability of average would be 0.18and of a flop 0.7. Ifthe criticissues a negative review,the probability of a hit drops to 0.03, the probability of average drops to 0.06, with flop increasing to 0.91. In addition, the probability of a positive review has been determined to be 0.25 and a negative review 0.75.The cost for the critic's review is $100,000.

a) Set up a decision tree with label decision and event nodes, and show terminal payoffs and event probabilities