# Probability Model; Decision Maker is Risk Neutral; Test Results

See attached file.

A decision maker is faced with the problem shown. Assume that the decision maker is risk neutral.

a) A test is available that will provide information about the possible outcomes associated with A. Add a branch called 'do the test' to the decisions below. Show how the test can be used to guide the selection of A or B. Previous evaluations of the test's performance indicate that when the outcome was 'good' the test indicated 'good' 90% of the time. Given that the outcome was 'bad', the test predicted 'bad' 40% of the time. What is the value of the information in the test? What is the optimal strategy for the decision maker to follow?

b) Suppose the test results in the past show that the test predicted 'good' 50% of the time when the outcome was 'good' and predicted 'bad' 50% of the time when the outcome was 'bad'. What is now the value of the information in the test? Why? What is the optimal strategy when this test is used?

c) What is the value of perfect information about outcome A?

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#### Solution Preview

See the attached file.

Probability Model

A decision maker is faced with the problem shown. Assume that the decision maker is risk neutral.

a) A test is available that will provide information about the possible outcomes associated with A. Add a branch called "do the test" to the decisions below. Show how the test can be used to guide the selection of A or B. Previous evaluations of the test's performance indicate that when the outcome was "good" the test indicated "good" 90% of the time. Given that the outcome was "bad", the test predicted "bad" 40% of the time. What is the value of the information in the test? What is the optimal strategy for the decision maker to follow?

First, we calculate the probabilities that the test performance would indicate "good" and "bad" outcome:

Test Forecast Event P(Event) P(Forecast/Event) P(Forecast and Event) P(Event/Forecast)

Good Good 0.6 0.9 =0.6*0.9=0.54 =0.54/0.78=0.69

Bad 0.4 0.6 0.24 0.31

P(Forecast is ...

#### Solution Summary

The solution determines the results of the test.