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 0.93 the test will detect it. If a bag does not contain large amounts of liquid, there is a 0.09 probability the test will conclude that it does (a false positive). Suppose that in reality only 5 in 100 bags actually contain large amounts of liquid.

1.What is the probability a randomly selected bag will have apositive test? Give your answer to four decimal places.

2.Given a randomly selected bag has a positive test, what is theprobability it actually contains a large amount of liquid? Giveyour answer to four decimal places.

3. Given a randomly selected bag has a positive test, what is theprobability it does not contain a large amount of liquid? Give youranswer to four decimal places.