Final answer:
Probability of Favorable Survey Result Given Favorable Market: 0.7
Probability of Favorable Survey Result Given Unfavorable Market: 0.2
Probability of Unfavorable Pilot Study Given Unfavorable Market: 0.9
Probability of Unfavorable Pilot Study Result Given Favorable Market: 0.2.
Step-by-step explanation:
To solve this problem, we need to create a decision tree and compute the expected monetary value (EMV) for each decision. Let's start by drawing the decision tree:
Decision Node: Jim's decision - Survey or Pilot Study
Chance Nodes: Market Favorable or Market Unfavorable
Terminal Nodes: Return of $100,000 or Loss of $60,000
Now, let's compute the revised probabilities needed to complete the decision and place these values in the decision tree:
Probability of Market Favorable: 0.5
Probability of Market Unfavorable: 0.5
Probability of Favorable Survey Result Given Favorable Market: 0.7
Probability of Favorable Survey Result Given Unfavorable Market: 0.2
Probability of Unfavorable Pilot Study Given Unfavorable Market: 0.9
Probability of Unfavorable Pilot Study Result Given Favorable Market: 0.2
Next, we calculate the EMV for each decision:
EMV of Survey: (0.7 * $100,000) + (0.3 * -$60,000) = $34,000
EMV of Pilot Study: (0.8 * $100,000) + (0.2 * -$60,000) = $72,000
Comparing the EMV of Survey ($34,000) to the EMV of Pilot Study ($72,000), it is clear that the best decision for Jim is to conduct the pilot study. The pilot study has a higher expected monetary value and is therefore the more favorable option.
Therefore,
Probability of Favorable Survey Result Given Favorable Market: 0.7
Probability of Favorable Survey Result Given Unfavorable Market: 0.2
Probability of Unfavorable Pilot Study Given Unfavorable Market: 0.9
Probability of Unfavorable Pilot Study Result Given Favorable Market: 0.2.
"Your question is incomplete, probably the complete question/missing part is:"
Jim Sellers is thinking about producing a new type of electric razor for men. If the market were favorable, he would get a return of $100,000, but if the market for this new type of razor were unfavorable, he would lose $60,000. Since Ron Bush is a good friend of Jim Sellers, Jim is considering the possibility of using Bush Marketing Research to gather additional information about the market for the razor. Ron has suggested that Jim use either a survey or a pilot study to test the market. The survey would be a sophisticated questionnaire administered to a test market. It will cost $5,000. Another alternative is to run a pilot study. This would involve producing a limited number of the new razors and trying to sell them in two cities that are typical of American cities. The pilot study is more accurate but is also more expensive. It will cost $20,000. Ron Bush has suggested that it would be a good idea for Jim to conduct either the survey or the pilot before Jim makes the decision concerning whether to produce the new razor. But Jim is not sure if the value of the survey or the pilot is worth the cost. Jim estimates that the probability of a successful market without performing a survey or pilot study is 0.5. Furthermore, the probability of a favorable survey result given a favorable market for razors is 0.7, and the probability of a favorable survey result given an unsuccessful market for razors is 0.2. In addition, the probability of an unfavorable pilot study given an unfavorable market is 0.9, and the probability of an unsuccessful pilot study result given a favorable market for razors is 0.2. (a) Draw the decision tree for this problem without the probability values. (b) Compute the revised probabilities needed to complete the decision, and place these values in the decision tree. (c) What is the best decision for Jim? Use EMV as the decision criterion.