Consider again the landowner’s decision problem described in Problem 39. Suppose now that, at a cost of $90,000, the landowner can request that a soundings test be performed on the site where natural...

Consider again the landowner’s decision problem described in Problem 39. Suppose now that, at a cost of $90,000, the landowner can request that a soundings test be performed on the site where natural gas is believed to be present. The company that conducts the soundings concedes that 30% of the time the test will indicate that no gas is present when it actually is. When natural gas is not present in a particular site, the soundings test is accurate 90% of the time.

a. Given that the landowner pays for the soundings test and the test indicates that gas is present, what is the landowner’s revised estimate of the probability of finding gas on this site?

b. Given that the landowner pays for the soundings test and the test indicates that gas is not present, what is the landowner’s revised estimate of the probability of not finding gas on this site?

c. Should the landowner request the given soundings test at a cost of $90,000? Explain why or why not. If not, at what price (if any) would the landowner choose to obtain the soundings test?