An oil well may be drilled on Mr. G's farm in LA. Based on what has happened to similar farms, we judge the probability of only oil being present to be. 3, the probability of only natural gas being present to be. 2, and the probability of neither being present to be. 5. Oil and gas never occur together. If oil is present, a geological test will give a positive result with probability. 8; if natural gas is present, it will give a positive result with probability. 2; and if neither are present, the test will be positive with probability. 1.
a. Model this problem as a Bayesian network over three variables: Oil, Gas, and Test.
b. Suppose the test comes back positive. What's the probability that ois is present?
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