Assignment:
An oil executive has determined that the probability that this oil field contains oil is 0.6. Before starting the drilling she decides to order a seismological test to see if there is oil in the ground. Unfortunately, the test is not entirely accurate. It concludes that there is oil with probability 0.9 if there is indeed oil in the ground. If there is no oil in the ground, it concludes so with probability 0.8. Suppose the test result come back positive (i.e., the test says there is oil in the ground). What is the probability that there is indeed oil in the ground given this test result?
Provide complete and step by step solution for the question and show calculations and use formulas.