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Probability and Decision Making

1- A pharmaceutical company conducted a study to evaluate the effect of an allergy relief medicine.
200 patients with symptoms that included itchy eyes and a skin rash received the new drug.

The results of the study are as follows:
90 of the patients treated experienced eye relief
135 had their skin rash clear up, and
54 experiences relief of both itchy eyes and skin rash.

? What is the probability that a patient who takes the drug will experience relief of at least one of the two symptoms?

2- Myrtle Air Express decided to offer direct service from Cleveland to Myrtle Beach. Management must decide between a full- price service using the company's new fleet of jet aircrafts and a discount service using smaller capacity commuter planes. It is clear that the best choice depends on the market reaction to the service Myrtle Air offers. Management developed estimates of the contribution to profit for each type of service based upon two possible levels of demand for service to Myrtle beach: strong and weak. The following table shows the estimated quarterly profits (in thousands of dollars):

Demand for service
Service Strong Weak
Full price $960 -$490
Discount $710 -$350

1. What is the decision to be made, what is the chance event, and what is the consequence for this problem? How many decision alternatives are there? How many outcomes are there for the chance event
2. If nothing is known about the probabilities of the chance outcomes, what is the recommended decision using the optimistic, conservative and minimax regret approaches
3. Suppose that management of Myrtle Air Express believes that the probability of strong demand is 0.77. Use the expected value approach to determine an optimal decision.

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Solution Summary

The solution contains a basic statistics problem using probability law and one Decision making problem using the optimistic, conservative, minimax regret and expected value approaches.