Question: Question 3: Suppose that you work for a global petroleum corporation that has recently bought offshore drilling rights off the New Jersey shoreline. If you drill for oil and you find oil, your company will make $9 million. But if you drill for oil and do not find oil, you will lose $4 million. You estimate there is a 30% chance of finding oil.

At a cost of $1.2 million, you can have seismic tests performed on your potential drilling site. These tests are not perfect. If there is oil at the site, there is an 80% chance that the test will be positive. If there is no oil at the site, there is a 90% chance that the test will be negative.

a) [10 points] What is the conditional probability of finding oil, given that the test is positive? What is the conditional probability of not finding oil, given that the test is negative?

b) [20 points] Construct a decision tree for this problem. Be sure to clearly mark the decisions, events, probabilities, and payoffs on the tree. Solve the tree to find the strategy that maximizes the expected earnings to the company. What is the optimal strategy?