Problem 2 (25 pts) To determine the probability that a drill hole contains oil, the following tests can be performed by a geologist A sonar scan test (TI) will indicate in 80% of all cases that oil is present if oil is present. The test will wrongly indicate that oil is present in 30% of all cases where there is no oil present. A core sample test (T2) will report in 90% of all cases that oil is present if oil is present. The test will wrongly indicate that oil is present in 60% of all cases where there is no oil present. From experience, the geologist knows that about 30% of all drill holes contain oil. a) Compute P(TI -ycs) and P(T2 ycs) b) What is the probability of oil given that a sonar scan test reported a positive test result? In other words, you should compute P(ContainOil TI-yes). Show how you compute it c) What is the probability of oil given that a core sample test reported a positive test result? In other words, you should compute P(ContainOil T2 yes). Show how you compute it What is the probability of oil given that both the sonar scan test and the core sample test indicate the presence of oil. You can assume that the two tests are conditionally independent? In other words, you should compute P(ContainOil T1-yes and T2-yes). Show how you compute it d)