An oil explorer orders seismic tests to determine whether oil is likely to be found in a certain drilling area. The seismic tests have a known reliability: when oil does exist in the testing area, the test will indicate so 90% of the time; when oil does not exist in the test area, 5% of the time the test will erroneously indicate that it does exist. The explorer believes that the probability of an oil deposit in the area is 0.4. If a test is conducted and indicates the presence of oil, what is the probability that an oil deposit exists? a. 0.9231 b. 0.9000 c. 0.8825 d. 0.8573 Contingency table: Test is positive Test is negative Total Oil exists 0.9 * 0.4 = 0.36 0.1 * 0.4 = 0.04 0.4 Oil does not exist 0.05 * (1 - 0.4) = 0.03 0.95 * (1 - 0.4) = 0.57 0.6 Total 0.39 0.61 1.0 P(Oil exists | The test is positive) = 0.36/0.39 = 0.9231 Option (a)
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