Question

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 0.97 the test will detect it. If a bag does not contain large amounts of liquid, there is a 0.1 probability the test will conclude that it does (a false positive). Suppose that in reality only 1 in 100 bags actually contain large amounts of liquid. a. What is the probability a randomly selected bag will have a positive test?

Answer 1

the probability is 0.1087 (10.87%)

Explanation:

defining the random variable T= the test is positive , then the probability that the test is positive given that a bag is chosen at random is

P(T)= probability of choosing a bag with large amounts of liquid * probability that the test is positive given that that the bag have excess liquid + probability of choosing a bag that does not have not large amounts of liquid * probability that the test is positive given that that the bag does not have not have excess liquid = 1/100 * 0.97 + 99/100 * 0.1 = 0.1087 (10.87%)