The Transportation Safety Authority (TSA) has developed a newtest to detect large amounts of liquid in luggage bags. Based onmany test runs, the TSA determines that if a bag does contain largeamounts of liquid, there is a probability of 0.9 the test willdetect it. If a bag does not contain large amounts of liquid, thereis a 0.09 probability the test will conclude that it does (a falsepositive). Suppose that in reality only 1 in 100 bags actuallycontain large amounts of liquid.
a. What is the probability a randomly selected bag will have apositive test? Give your answer to four decimal places.
b. Given a randomly selected bag has a positive test, what isthe probability it actually contains a large amount of liquid? Giveyour answer to four decimal places.
c. Given a randomly selected bag has a positive test, what isthe probability it does not contain a large amount of liquid? Giveyour answer to four decimal places.
