A large midwestern bank has devised a math aptitude test that it claims provides valuable input into the hiring decision for bank tellers. The bank's research indicates that 60 percent of all tellers hired by midwestern banks are classified as performing satisfactorily in the position at their initial 6-month performance review, while the rest are rated as unsatisfactory. Of the tellers whose performance is rated as satisfactory, 90 percent had passed the math aptitude test. Of the tellers who were rated unsatisfactory, only 20 percent had passed the math aptitude test.

a. What is the probability that a teller would be rated as satisfactory at her 6-month performance review, given that she passed the math aptitude test?

b. What is the probability that a teller would be rated as satisfactory at her 6-month performance review, given that she did not pass the math aptitude test?

c. Does the test seem to be an effective screening device to use in hiring tellers for the bank? Why or why not?