An oil wildeat driller must decide either to drill or not to drill . He is uncertain whether the hole is dry, wet, or soaking. His payoffs are given in Table II.1. The cost of drilling is uncertain and will either be $40,000 with probability .2, $50,000 with probability .7 or $70,000 with probability .1.

In order to gain more information before deciding to drill, at a cost of $10,000 the wildcatter could take seismic soundings which will determine exactly the underground geological structure as either being (a) no structure (Outcome NS which is bad), or (b) open structure (Outcome OS which is so-so), or closed structure (Outcome CS which is really hopeful). The geological experts have provided the wildcatter with Table II. 2 which shows the joint probability distribution of the underlying geological structure and the State of a randomly drilled well.

Alternatively, for a cost of $3,000, the geologists can do a much less accurate test which does not determine the underground geological structure exactly. Table II.3

illustrates the accuracy of this cheaper test.

Assignment:

1. Assume you are making your decision on the basis of expected value of the return on investment (i.e. you are ignoring risk), determine using the methods developed in this course whether or not you would drill the well.
2. Determine, using the methods discussed in this course, whether or not it would be worthwhile to do either the more costly or the less costly test.
3. Explain your reasoning in detail (preferably along with a decision tree of the situation) and back up your arguments using the data provided.

Hints:

1. From your decision point of view there are basically six decisions which are the combinations of drilling or not drilling along with either doing no testing, doing the accurate but expensive test, or the less accurate but cheaper test. You must which of these six choices is the best.
2. If you order either of the two tests, you will not decide to drill until you have received the results of the test.
3. Draw your decision tree first and then figure out what probabilities you need to compute.
4. The "exact" test tells you exactly what is underground from which you can figure out the conditional probabilities of the wellbeing dry, wet, or soaking. The "inexact" test only tells you what is thought to be underground from which you need to find the conditional probabilities of what is actually underground from which you then figure out the conditional probabilities of the wellbeing dry, wet, or soaking.

Price: $13.86

Solution: The downloadable solution consists of 8 pages, 586 words and 5 charts.
Deliverable: Word Document