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)
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...
Related questions
Question
Plese, answer me immediately
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
×
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps with 6 images
Recommended textbooks for you
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON
A First Course in Probability (10th Edition)
Probability
ISBN:
9780134753119
Author:
Sheldon Ross
Publisher:
PEARSON