A network earns $2.5 million dollars each season for a hit program and loses $0.5 million each season for a flop. In general, 19% of the programs are considered hits and 81% of the programs are flops. If the network does not make any program, no profit will be earned.
At a cost of $400,000, a research firm will analyze the pilot episode and issue a report predicting whether the program is going to be a hit or a flop. From the past data, if the program is going to be a hit, there is a 90% chance that the research firm predicted it is going to be a hit. On the other hand, there is a 20% chance the research firm predicted that the program is going to be a hit, but ended as a flop.
(1) Construct the 3rd decision tree that has both "No Any Information" and the "Research Firm" decision alternatives. Be careful to calculate the appropriate probabilities and to include them in the decision tree.
(2) Based on (1), calculate the EVII.
(3) Based on (2), what should the network do? Should the network pay to consult the research firm? Why or Why not. Please explain in detail.