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.

1) What is the probability a randomly selected bag will have a positive test = 0.132

2) what is the probability it actually contains a large amount of liquid = 0.3522

3) what is theprobability it does not contain a large amount of liquid = 0.6477

Step-by-step explanation:

The detailed explanation using the bayes rule is as shown in the attachment.

geometric series converge the common ratio r has magnitude less than one.

which is equivalent to

for the example we need

|2-x| < 1

-1 < 2-x   and 2-x < 1

x < 3 and x > 1

we can write that

answer: 1 < x < 3

1a. common ratio r=250/25=10 > 1     diverges

1b.   r=50/100=1/2 converges

when these converge they converge to

where a is the first term.

answer: 200

1c. r=-1   so it's not the case that |r| < 1.     diverges

2a. x is the common ratio so we converge when |x|< 1

2b.   r=-10x / -2 = 5x.

we converge when

|5x| < 1

|x| < 1/5

2c.   r=3-2x

-1 < 3-2x and 3-2x < 1

-4 < -2x and 2 < 2x

x < 2 and 1 < x

1 < x < 2

2d. [/tex] r=-48x^3/12 = 4x^3[/tex]

|4x^3| < 1

|x^3| < \frac 1 4

|x| < 4^{-1/3}

.95

step-by-step explanation: