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?

Question

Mathematics

Dustin Russo

17 June, 09:01

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?

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Answers (1)

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Seth Mcmahon · Answer 1

the probability is 0.1087 (10.87%)

Step-by-step 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%)