_{Applicants who wish to be admitted ta a certain professional school in a large university are required to take a screening test devised by an educational testing service. From past results , the testing service has estimated that 70% of all applicants are eligible for admission and that 92% of those who are eligible for admission pass the exam, whereas 12% of those who are ineligible for admission pass the exam. Using these results, what is the probability that an applicant for admission:}

_{a) passed the exam}

_{b) passed the exam, but was actually ineligible?}