# Probability and Business Decisions

a. See the attached file for the chart of data pertaining to this question.

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?

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#### Solution Preview

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?

Expected payoff = SPi*Xi

Where Pi=Probability of state of nature i

Xi=payoff under state of nature I

Expected payoff A1 = 0.2*3000+0.5*2000+0.3*(-6000) = -200

Expected payoff A2 = 0.2*0+0.5*0+0.3*0 = 0

What would be your recommendation? Interpret the results based on practical considerations.

As the expected payoff is higher when the decision not to sell juices is taken, I recommend a decision for not selling juices.

The practical consideration is that if we decide to ...

#### Solution Summary

This solution illustrates a simple and systematic way to show how decision-making can be done when choices are made under uncertainty. The concepts of probability and expected payoff are used to select the best alternative for the CoffeeTime. The post also discusses the practical considerations along with financial considerations while taking a decision. In the second part, it discusses how the city specific information on the profits can or cannot be used for taking decision in another city