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A real estate developer is planning to build a condominium development in a resort community. The company is trying to decide between building a small, medium, or large development. The payoffs (in $1,000s) received for each size of development will depend on the market demand for condominiums in the area, which could be low, medium, or high. The payoff matrix for this decision problem is: (Payoffs in $1,000s) Market Demand Size of Development Low Medium High Small 450 450 450 Medium 250 550 550 Large -350 350 850 The company estimates a 20% chance that market demand will be low, a 35% chance that it will be medium, and a 45% chance that it will be high. The developer can hire a consultant to predict the most likely level of demand for this project. This consultant has done many similar studies and has provided the developer with the following joint probability table summarizing th accuracy of the results. Forecasted Demand Low Low Medium Actual Demand Medium High 0.1600 0.0100 0.0300 0.0420 0.2660 0.0420 High 0.0135 0.0360 0.4005 The sum of the entries on the main diagonal of this table indicates that the consultant's forecast is correct about 82.65% of the time, overall. (a) Construct the conditional probability table showing the probabilities of the various actual demands given each of the forecasted demands. Actual Demand Forecasted Demand Low Medium High Low 0.7422 × 0.0319 0.0636 x Medium 0.1949 × 0.8493 0.0890 High 0.0628 × 0.1151 x 0.8474

A real estate developer is planning to build a condominium development in a resort community. The company is trying to decide between building a small, medium, or large development. The payoffs (in $1,000s) received for each size of development will depend on the market demand for condominiums in the area, which could be low, medium, or high. The payoff matrix for this decision problem is: (Payoffs in $1,000s) Market Demand Size of Development Low Medium High Small 450 450 450 Medium 250 550 550 Large -350 350 850 The company estimates a 20% chance that market demand will be low, a 35% chance that it will be medium, and a 45% chance that it will be high. The developer can hire a consultant to predict the most likely level of demand for this project. This consultant has done many similar studies and has provided the developer with the following joint probability table summarizing th accuracy of the results. Forecasted Demand Low Low Medium Actual Demand Medium High 0.1600 0.0100 0.0300 0.0420 0.2660 0.0420 High 0.0135 0.0360 0.4005 The sum of the entries on the main diagonal of this table indicates that the consultant's forecast is correct about 82.65% of the time, overall. (a) Construct the conditional probability table showing the probabilities of the various actual demands given each of the forecasted demands. Actual Demand Forecasted Demand Low Medium High Low 0.7422 × 0.0319 0.0636 x Medium 0.1949 × 0.8493 0.0890 High 0.0628 × 0.1151 x 0.8474

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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A real estate developer is planning to build a condominium development in a resort community. The company is trying to decide between building a small, medium, or large development. The payoffs (in $1,000s) received for each size of development will depend on the market demand for condominiums in the area, which could be low, medium, or high. The payoff matrix for this decision problem is: (Payoffs in $1,000s) Market Demand Size of Development Low Medium High Small 450 450 450 Medium 250 550 550 Large -350 350 850 The company estimates a 20% chance that market demand will be low, a 35% chance that it will be medium, and a 45% chance that it will be high. The developer can hire a consultant to predict the most likely level of demand for this project. This consultant has done many similar studies and has provided the developer with the following joint probability table summarizing the accuracy of the results. Actual Demand Forecasted Demand Low Medium High Low 0.1600 0.0100 0.0300 Medium 0.0420 0.2660 0.0420 High 0.0135 0.0360 0.4005 The sum of the entries on the main diagonal of this table indicates that the consultant's forecast is correct about 82.65% of the time, overall. (a) Construct the conditional probability table showing the probabilities of the various actual demands given each of the forecasted demands. Actual Demand Forecasted Demand Low Medium High Low 0.7422 × 0.0319 × 0.0636 × Medium 0.1949 × 0.8493 × 0.0890 × High 0.0628 × 0.1151 × 0.8474 ×
Transcribed Image Text:A real estate developer is planning to build a condominium development in a resort community. The company is trying to decide between building a small, medium, or large development. The payoffs (in $1,000s) received for each size of development will depend on the market demand for condominiums in the area, which could be low, medium, or high. The payoff matrix for this decision problem is: (Payoffs in $1,000s) Market Demand Size of Development Low Medium High Small 450 450 450 Medium 250 550 550 Large -350 350 850 The company estimates a 20% chance that market demand will be low, a 35% chance that it will be medium, and a 45% chance that it will be high. The developer can hire a consultant to predict the most likely level of demand for this project. This consultant has done many similar studies and has provided the developer with the following joint probability table summarizing the accuracy of the results. Actual Demand Forecasted Demand Low Medium High Low 0.1600 0.0100 0.0300 Medium 0.0420 0.2660 0.0420 High 0.0135 0.0360 0.4005 The sum of the entries on the main diagonal of this table indicates that the consultant's forecast is correct about 82.65% of the time, overall. (a) Construct the conditional probability table showing the probabilities of the various actual demands given each of the forecasted demands. Actual Demand Forecasted Demand Low Medium High Low 0.7422 × 0.0319 × 0.0636 × Medium 0.1949 × 0.8493 × 0.0890 × High 0.0628 × 0.1151 × 0.8474 ×
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