1. Applicants for temporary office work at Carter Temporary Help Agency who have successfully completed an administrative assistant course are then placed in suitable positions by Nancy Dwyer and Darla Newberg. Employers who hire temporary help through the agency return a card indicating satisfaction or dissatisfaction with the work performance of those hired. From past experience it is known that 80% of the employees placed by Nancy are rated as satisfactory, and 55% of those placed by Darla are rated as satisfactory. Darla places 65% of the temporary office help at the agency, and Nancy places the remaining 35%. If a Carter office worker is rated unsatisfactory, what is the probability that he or she was placed by Darla? (Round your answer to three decimal places.)
2. Urn A contains seven white balls and six black balls. Urn B contains three white balls and four black balls. A ball is drawn from Urn A and then transferred to Urn B. A ball is then drawn from Urn B. What is the probability that the transferred ball was white given that the second ball drawn was white? (Round your answer to three decimal places.)

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 0.94. However, the probability that the test will erroneously indicate the presence of the disease in those who do not actually have it is 0.06. It is estimated that 5% of the population who take this test have the disease. (Round your answers to three decimal places.)

(a) If the test administered to an individual is positive, what is the probability that the person actually has the

disease?

(b) If an individual takes the test twice and the test is positive both times, what is the probability that the person

1. actually has the disease? (Assume that the tests are independent.)