The Transportation Safety Authority (TSA) has developed a new test to detect large amounts of liquid in luggage bags. Based on many test runs, the TSA determines that if a bag does contain large amounts of liquid, there is a probability of 0.96 the test will detect it. If a bag does not contain large amounts of liquid, there is a 0.06 probability the test will conclude that it does (a false positive). Suppose that in reality only 3 in 100 bags actually contain large amounts of liquid. Required:
a. What is the probability a randomly selected bag will have apositive test?
b. Given a randomly selected bag has a positive test, what is theprobability it actually contains a large amount of liquid?
c. Given a randomly selected bag has a positive test, what is theprobability it does not contain a large amount of liquid?