The oil company Trou Noir is considering drilling a well in a remote location in Alberta. The cost of drilling is $70,000. This amount will be lost if the well is "dry". Otherwise, the well will be called "wet" if it contains a little oil or "soak" if it contains a lot. The gross income associated with a wet well is $220,000 ($150,000 if we subtract the cost of drilling) and that associated with a quench well is $670,000 ($600,000 if we subtract the cost of drilling). The company's geologist, Diane Martin, was consulted to estimate the probabilities for each of the above events ("dry", "wet", "soak"). She mentions that such probabilities depend on the shale structure beneath the drilling site. If this structure forms a dome, the chances of oil being drawn from it are significantly higher than if such a dome does not exist. Ms. Martin estimates a 60% probability that the shale structure will form a dome in the location under which Trou Noir plans to drill. She also estimated the following probabilities for each of the events, conditional on the presence or absence of a dome.

 

Drilling result	Presence of a dome	Absence of dome
Dry well	0.60	0.85
Wet well	0.25	0.125
Quenching well	0.15	0.025

 

Finally, Ms. Martin suggests that Trou Noir consider doing a seismic test on the site before starting to drill. This test would cost $10,000 and would make it possible to better estimate the presence of a dome, without providing 100% assurance of its presence or absence. It evaluates the reliability of this test with the following conditional probabilities:

 

Pr (Test indicates "Dome" | Presence of a dome) = 0.90
Pr (Test indicates "No dome" | Presence of a dome) = 0.10
Pr (Test indicates "Dome" | Absence of a dome) = 0.20
Pr (Test indicates "No dome" | Absence of a dome) = 0.80

Draw and solve the decision tree to help Trou Noir develop a strategy that maximizes its expected income. This strategy should specify whether Trou Noir should do the seismic test and under what conditions we should or should not drill.