Mr. Schellburger, the CEO of Schellburger Oil, is a risk- neutral person. He is facing a dilemma - He is not sure whether or not he should drill an oil well. His decision situation is captured by the following decision tree (all prospects are expressed in millions of dollars): [oil [ &]= 0.4 $50 Drill (No Oil | &)= 0.6 $15 A No Oil SO Do Not Drill PART I: Given the above information, answer the below questions. a) What types of nodes are A and B? |A is a chance node and B is a value node b) Without any additional information, what will he choose? Drill c) What is the value of his current decision? (Round up to 2 decimal places) millions.PART II: Fortunately, Mr. Schellburger has access to a detector which can give him some further information on whether or not the site contains oil. The detector is symmetric and has an accuracy of 0.90. For this example, the distinction of interest is whether oil is present (2 degrees: Oil or No Oil) and the observed distinction is the result of the test. Let "Oil" be a test result indicating that oil is present and "No Oil" be a test result that no oil is present. Consider the following incomplete Assessed Form probability tree. Assessed Form: "Oil" {oil"[ oil,&]= foil,"oil" [ &}= Oil [oil | &}= 0.4 ("No oil" [ oil, & }= {Oil,"No oil" | &}= "No Oil' "Oil" ("oil" [ No Oil,&]= {No oil,"oil" | &}= {No Oil | &]= 0.6 No Oil ("No Oil" ( No Oil,&]= (No Oil, "No Oil"|&}= "No Oil" d) What is the sensitivity of the detector? (Round up to 2 decimal places) e) What is the value of the elemental probability {Oil, "Oil"|&}? (Round up to 2 decimal places)Consider the following incomplete Inferential Form probability tree. Inferential Form: Oil [oil | "oil"&}= ("oil", oil [ &)= "oil" {"oil"| &)= (No oil | "oil", & }= ("oil",No Oil [ &]= No oil Oil [oil| "No Oil" & }= ("No Oil", oil | &}= ("No Oil"[ &)= "No Oil" B (No Oil | "No oil", &}= ("No Oil",No Oil | &)= No oil f) Mr. Schellburger decides to use the detector. It indicates that "Oil". How likely is it that oil is actually present underneath the site, given this signal? (Round up to 2 decimal places) g) Mr. Schellburger decides to use the detector. It indicates that "No Oil". How likely is it that oil is actually present underneath the site, given this signal? (Round up to 2 decimal places) h) What is the value of the decision, given the "Oil" signal?(Round up to 2 decimal places) millions i) What is the value of the decision, given the "No Oil" signal?(Round up to 2 decimal places) millions i) What is the most Mr. Schellburger is willing to pay for the use of the detector (i.e., the value of imperfect information)? (Round up to 2 decimal places) millions