In the oil-wildcatting problem, suppose that the company could collect information from a drilling core sample and analyze it to determine whether a dome structure exists at Site 1. A positive result would indicate the presence of a dome, and a negative result would indicate the absence of a dome. The test is not perfect, however. The test is highly accurate for detecting a dome; if there is a dome, the test shows a positive result 99% of the time. On the other hand, if there is no dome, the probability of a negative result is only 0.85. Thus, P(+ 1 Dome) 0.99 and P(-1 No Dome) = 0.85. Use these probabilities, the information given in the example, and Baye's theorem to find the posterior probabilities P(Dome 1 +) and P(Dome 1 -). If the test Rives a positive result, which site should be selected? Calculate expected values to support your conclusion. If the test result is negative, which site should be chosen?