An oil explorer must decide whether to drill on a site before her option expires or to abandon her rights to the site. D

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An oil explorer must decide whether to drill on a site before
her option expires or to abandon her rights to the site. Drilling
an oil well costs $100,000. If oil is found, the explorer will sell
and make a net profit of $500,000 (this includes the cost of
drilling). The explorer can hire a geologist to take a seismic test
of the site at a cost of $10,000. Such test reveals, with
certainty, whether the geophysical substructure of the land is of
type A, type B, or type C, where each type has a different degree
of possibility for the existence of oil. From past experience, the
probability that a certain substructure will occur, given that oil
exists, is P[type A | oil] = 14/28 P[type B | oil] = 9/28 P[type C
| oil] = 5/28 The prior probabilities for the three substructures
at the site are P[type A] = 0.20 P[type B] = 0.30 P[type C] = 0.50
Given that the prior probability P[oil] = 0.28 (a) Draw a fully
described decision tree for deciding whether (1) the explorer
should make the seismic test and (2) should drill for oil or
abandon the site following the decision to test or not. In taking
the seismic test, the decision about drilling will be made knowing
the substructure that exists. (b) Calculate the monetary outcomes
(use the explorer’s change in assets) of each path on the tree and
place each at the end of appropriate path. Remember that taking the
test incurs extra costs. (c) Taking the test improves knowledge
about the existence of oil. Calculate the probabilities of finding
oil in each of the three types of substructures (i.e., P[oil | type
A], P[oil | type B], and P[oil | type C]) (d) Label each chance
branch in the tree from (a) with its probability of occurring (e)
What strategy should the explorer follow? To pay for the seismic
test? To drill for oil without taking the test? What decision
should be made following the test? (f) What is the maximum amount
the explorer should pay for the seismic test? (i.e., what is the
expected value of sample information, EVSI?) (g) What is the
expected value of perfect information (EVPI) about the existence of
oil?