Question: The NBS television network is considering picking up a new show called "Dancing With The Millionaires". NBS earns an average of $4 million from a hit show and loses an average of $1 million on a flop. Historically, 25% of all the new shows picked up by the network turn out to be hits and 75% turn out to be flops.

1. Based on the expected monetary value (EMV) criterion, should the network pick up "Dancing With The Millionaires"?
2. What is the expected value of perfect information (EVPI) in this case?
   For $200,000 a market research firm will have audiences in several different cities view a pilot of a proposed new show. The firm then interviews the audience members and uses the information to predict whether the show will be a hit or a flop. NBS has used this market research firm many times before. Out of 100 shows that turned out to be hits, the market research firm predicted that 90 of them would be hits. Out of 100 shows that turned out to be flops, the market research firm predicted that 80 of them would be flops. Thus, NBS believes that the market research firm's predictions have the following properties: \(p\) (firm predicts hit | show will be a hit) \(=0.90\) and \(p(\) firm predicts flop | show will be a flop \()=0.80\).
3. Based on the information given above, what is the probability that the market research firm will predict that "Dancing With The Millionaires" will be a hit?
4. If the market research firm predicts that "Dancing With The Millionaires" will be a hit, what is the probability that it actually will be a hit?
5. Using a decision tree and the EMV criterion, determine whether or not NBS should hire the market research firm to predict whether "Dancing With The Millionaires" will be a hit or flop.

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