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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