The Transportation Safety Authority (TSA) has developed a new test to detect large amounts of liquid...

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 0.9 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 1 in 100 bags actually contain large amounts of liquid.

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

b. Given a randomly selected bag has a positive test, what is the probability it actually contains a large amount of liquid? Give your answer to four decimal places.

c. Given a randomly selected bag has a positive test, what is the probability it does not contain a large amount of liquid? Give your answer to four decimal places.

Solutions

Expert Solution

answer:

given data,

probaility of genuine positve i,e likelihood that it test recognizes effectively

Probabiility(true)=0.9

probability of false positive i,e likelihood that test distinguishes erroneously

Probability(false)=0.09

likelihood of substantial fluid amount

Probability (large quantity)=P(1)=1/100=0.01

likelihood of little fluid amount

Probability(small quantity)=P(2)=99/100=0.99

now,

orchestra answered 9 months ago

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