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 75% 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.)
P(Darla) = 0.65
P(Nancy) = 0.35
P(unsatisfactory | Nancy) = 1 - 0.75 = 0.25
P(unsatisfactory | Darla) = 1 - 0.55 = 0.45
Bayes' Theorem: P(A | B) = P(A & B)/P(B)
P(Darla | unsatisfactory) = P(Darla and unsatisfactory)/P(unsatisfactory)
= (0.65x0.45)/(0.65x0.45 + 0.35x0.25)
= 0.770
Applicants for temporary office work at Carter Temporary Help Agency who have successfully
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