1. (40%) Bubba Wildcat has the opportunity to buy a tract of land underwhich he believes there is oi

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1. (40%) Bubba Wildcat has the opportunity to buy a tract of land underwhich he believes there is oil with 0.40 probability and natural gas with0.60 probability. After buying the land he can choose to make a testdrill for $10,000 to gather more information. A “positive” resultindicates there is oil. The false positive rate is 20%, and the falsenegative rate is 10%.The expected cost of full-scale drilling is $100,000 regardless ofwhether there is oil or gas or whether he made a test drill or not. Ifoil is discovered, Bubba will receive an expected income of $150,000above the cost of the land. If natural gas is discovered, then Bubbawill 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 forBubba. Show your calculations!2. (25%) Jason is indifferent between $10 for sure and a lottery thatpays $100 with probability 0.09 and $0 with probability 0.91. He is alsoindifferent between $70 for sure and a lottery that pays $100 withprobability 0.80 and $0 with probability 0.20. Jason is given a choicebetween lottery A or B:Y = {$100, $70, $10, $0}pA = (0.10, 0.20, 0.70, 0 )pB = ( 0, 0.40, 0.50, 0.10)If Jason’s preferences are complete, transitive, continuous andmonotone, and satisfy the substitution axiom,(a) will he prefer lottery A or B? Show your work.(b) Is Jason risk averse, risk neutral, or risk loving?3. (15%) Briefly define the following terms:a) an information set;b) perfect recall;c) a lottery (use math)4. (15%) Irene has committed to meeting a friend at an out of townrestaurant tonight. However, she thinks there is a 20% chance her carbattery is bad, and if it is bad, she believes she has a 75% chance ofbeing stranded tonight. On the other hand, if the battery is good, thenthere is no chance she will be stranded tonight. A local service stationoffers a battery testing service for $10. Their brochure states that 99%of good batteries pass the test, while 90% of bad batteries fail thetest.(a) If Irene has her battery tested, what is the probability it willpass the test?(b) If Irene has her battery tested and it passes, what is theprobability her battery is good?(c) If Irene has her battery tested and