The Mobile Oil company has recently acquired oil rights to a new potential source of natural oil in Alaska. The current market

value of these rights is $$80,000.$ If there is natural oil at the site, it is estimated to be worth $$900,000$; however, the company

would have to pay $$100,000$ in drilling costs to extract the oil. The company believes there is a $0\mathrm{.}22$ probability that the proposed

drilling site actually would hit the natural oil reserve. Alternatively, the company can pay $$30,000$ to first carry out a seismic

survey at the proposed drilling site. The probability of a favorable seismic survey when oil is present at the drilling site is $0\mathrm{.}6.$ The

probability of an unfavorable seismic survey when no oil is present is $0\mathrm{.}80.$

$($a$)$ What is the probability of a favorable seismic survey?

$($b$)$ What is the probability of an unfavorable seismic survey?

$($c$)$ Construct a decision tree for this problem. What is the optimal decision strategy using the EMV criterion?

The company should conduct the survey and make a decision based on the results.

The company should drill at the location without conducting the survey.

The company should sell the drilling rights at the current location without conducting a survey.

$($d$)$ To which financial estimate in the decision tree is the EMV most sensitive$?$

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