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 85% of the time; when oil does not exist in the test area, 10% of the time the test will erroneously indicate that it does exist.
The explorer believes that the probability of existence of an oil deposit in the test area is 0.4. If a test is conducted and indicates the presence of oil, what is the probability that an oil deposit really exists?