1.

A medical test has been designed to detect the presence of a certain disease. Among people who have the disease, the probability that the disease will be detected by the test is 0.9. However, among those who do not have the disease, the probability that the test will detect the presence of the disease is 0.06. It is estimated that 6% of the population who take this test actually have the disease. (Round your answers to three decimal places.)

(a) If the test administered to an individual is positive (the disease is detected), what is the probability that the person actually has the disease? (b) If the test administered to an individual is negative (the disease is not detected), what is the probability that the person actually does have the disease?

2.

Box A contains seven white marbles and six black marbles. Box B contains four white marbles and three black marbles. An experiment consists of first selecting a marble at random from Box A. The marble is transferred to Box B and then a second marble is drawn from Box B. What is the probability that the first marble was white given that the second marble was white? (Round your answer to three decimal places.) 3.

Three machines turn out all the products in a factory, with the first machine producing 35% of the products, the second machine 15%, and the third machine 50%. The first machine produces defective products 4% of the time, the second machine 5% of the time and the third machine 20% of the time. What is the probability that a non-defective product came from the second machine? (Round your answer to four decimal places.)