An offshore concession in the China Sea was evaluated by an

An offshore concession in the China Sea was evaluated by an oil company, whose geologists postulated three possible analogs for the habitat of the petroleum in the concession: the geologic setting of the concession might be similar to (1) an oil-bearing area in the Xian province where the exploration success ratio is 20%, (2) the Gulf of Tonkin, which has a success ratio of only 10%, or (3) the Java Sea, which has a highly favorable success ratio of 35%. The geologists subjectively assigned a likelihood of 0.7 that the concession would prove to be like the Xian province, 0.10 that it would be like the Gulf of Tonkin, and 0.2 that it would be like the Java sea. The first four exploratory wells drilled in the concession resulted in 3 successes. How should the likelihoods assigned to the three possible analog areas be revised in light of this outcome?

Solution

Event Prior Conditional Joint Revised Probability Xian Province 0.7 0.2 0.14 0.6363 Gulf of Tonkin 0.1 0.1 0.01 0.0454 Java Sea 0.2 0.35 0.07 0.3181 0.22