Statistics need help

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 0.07 probability the test will conclude that it does (a false positive). Suppose that in reality only 4 in 100 bags actually contain large amounts of liquid.

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

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.

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.

P[true positive] = 0.9*0.04 = T
Pfalse positive] = 0.07*0.96 = F

a. P[positive] = T + F = 0.1032 <-----

b. P[ T | positive] = T/0.1032 = 0.3488 <------

c. P[ F | positive] = 1 - 0.3488 = 0.6512 <-------
(or compute F/0.1032 = 0.6512)

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