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A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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3. The Miramar Company is going to introduce one of three new products: a widget, a hummer, or a nimnot. The market conditions (favorable, stable, or unfavorable) will determine the profit or loss the company realizes, as shown in the following payoff table: Market Conditions Favorable Stable Unfavorable Product .2 .7 .1 Widget $120,000 $70,000 $-30,000 Hummer 60,000 40,000 20,000 Nimnot 35,000 30,000 30,000 a. Compute the expected value for each decision and select the best one. b. Develop the opportunity loss table and compute the expected opportunity loss for each product. c. Determine how much the firm would be willing to pay to a market research firm to gain better information about future market conditions. d. The Miramar Company is considering contracting with a market research firm to do a survey to determine future market conditions. The results of the survey will indicate either positive or negative market conditions. There is a 0.60 probability of a positive report, given favorable conditions; a 0.30 probability of a positive report, given stable conditions; and a 0.10 probability of a positive report, given unfavorable conditions. There is a 0.90 probability of a negative report, given unfavorable conditions; a 0.70 probability, given stable conditions; and a 0.40 probability, given favorable conditions. Using decision tree analysis and posterior probability tables, determine the decision strategy the company should follow, the expected value of the strategy, and the maximum amount the company should pay the market research firm for the survey results.
Transcribed Image Text:3. The Miramar Company is going to introduce one of three new products: a widget, a hummer, or a nimnot. The market conditions (favorable, stable, or unfavorable) will determine the profit or loss the company realizes, as shown in the following payoff table: Market Conditions Favorable Stable Unfavorable Product .2 .7 .1 Widget $120,000 $70,000 $-30,000 Hummer 60,000 40,000 20,000 Nimnot 35,000 30,000 30,000 a. Compute the expected value for each decision and select the best one. b. Develop the opportunity loss table and compute the expected opportunity loss for each product. c. Determine how much the firm would be willing to pay to a market research firm to gain better information about future market conditions. d. The Miramar Company is considering contracting with a market research firm to do a survey to determine future market conditions. The results of the survey will indicate either positive or negative market conditions. There is a 0.60 probability of a positive report, given favorable conditions; a 0.30 probability of a positive report, given stable conditions; and a 0.10 probability of a positive report, given unfavorable conditions. There is a 0.90 probability of a negative report, given unfavorable conditions; a 0.70 probability, given stable conditions; and a 0.40 probability, given favorable conditions. Using decision tree analysis and posterior probability tables, determine the decision strategy the company should follow, the expected value of the strategy, and the maximum amount the company should pay the market research firm for the survey results.
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