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# CoffeeTime Probability Theory in Decision Making simulation

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Run the "Probability Theory in Decision Making" simulation and then answer the following questions, in short answer format:

a. CoffeeTime is considering selling juices along with its other products.
States of Nature
High Sales Med. Sales Low Sales
A(0.2) B(0.5) C(0.3)
A1 (sell juices) 3000 2000 -6000
A2 (don't sell juices) 0 0 0

The probabilities shown above represent the states of nature and the decision maker's (e.g., manager) degree of uncertainties and personal judgment on the occurrence of each state. What is the expected payoff for actions A1 and A2 above? What would be your recommendation? Interpret the results based on practical considerations.

b. Bayes and empirical Bayes (EB) methods structure combining information from similar components of information and produce efficient inferences for both individual components and shared model characteristics. For example, city-specific information on the profits involved in selling a particular brand of coffee in Mumbai might be unavailable. How could CoffeeTime "borrow information" from adjacent cities or other countries to employ Bayesian logic?

Finally, what additional strategy (or variation on a given strategy) would you recommend to the key decision maker in the simulation to solve the challenge given? Prepare a 350-word memo to the simulation's key decision maker advocating your recommendation

#### Solution Preview

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Run the "Probability Theory in Decision Making" simulation and then answer the following questions, in short answer format:
a. CoffeeTime is considering selling juices along with its other products.
States of Nature
High Sales Med. Sales Low Sales
A(0.2) B(0.5) C(0.3)
A1 (sell juices) 3000 2000 -6000
A2 (don't sell juices) 0 0 0

The probabilities shown above represent the states of nature and the decision maker's (e.g., manager) degree of uncertainties and personal judgment on the occurrence of each state. What is the expected payoff for actions A1 and A2 above? What would be your recommendation? Interpret the results based on practical considerations.

Probability
A B C
0.2 0.5 0.3
Payoff
A1 (sell juices) 3000 2000 -6000
Probability x Payoff 600 1000 -1800

A2 (don't sell juices) 0 0 0
Probability x Payoff 0 0 0

Expected payoff for action ...

#### Solution Summary

Detailed answers to the questions and sample memo.

\$2.19