Bubba Wildcat has the opportunity to buy a tract of land under which he believes there is oil with 0.40 probability and natural gas with 0.60 probability. After buying the land he can choose to make a test drill for $10,000 to gather more information. A "positive" result indicates there is oil. The false positive rate is 20%, and the false negative rate is 10%.
The expected cost of full-scale drilling is $100,000 regardless of whether there is oil or gas or whether he made a test drill or not. If oil is discovered, Bubba will receive an expected income of $150,000 above the cost of the land. If natural gas is discovered, then Bubba will receive an expected income of $50,000 above the cost of the land. Assume Bubba is risk neutral. Draw a decision tree, and solve for an optimal decision plan for Bubba.