(07) A hiring manager of an engineering firm classified the applications for mechanical engineering positions in her firm into three groups: group 1 (recent graduates with exceptional GPA), group 2 (graduates with moderate work experience), and group 3 (no college degree, but exceptionally experienced in the relevant field). Of the applicant pool, 30% came from group 1, 40% came from group 2, and 30% came from group 3. By experience, she knows 80% of group 1 applicants, 60% of group 2 applicants, and 90% of group 3 applicants are likely to be selected. The total probability of an applicant being selected to the firm is:
[5 Points]
(a) 75%
(b) 43%
(c) 25%
(08) Problem (07) continued: if the performance of a new recruitment will be evaluated after 1 year, what is the probability that the evaluated candidate would be from group 1, given that the applicant was selected to the position?
[5 Points]
(a) 80%
(b) 32%
(c) 24%