# Bayesian Probability Theory

The original questions were:

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?

The questions above were answered in the attached file below. My question that I am submitting for this problem is to expand on the above situation by recommending an additional strategy (or variation on a given strategy) to solve the challenge given?

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#### Solution Summary

Bayesian Probability Theory is discussed as CoffeeTime is considering selling juice and other products. An analysis is given to determine whether this is feasible.