1. A psychologist developed a test designed to help predict whether production-line workers in a large industry will perform satisfactorily. A test was administered to all new employees in a corporation. At the end of the first year of work, these employees were rated by their supervisors: 18% were rated excellent, 53% were rated satisfactory and 29% were rated poor. 48% percent of those rated excellent passed the psychologist's test, as did 22% of those rated satisfactory and 12% of those rated poor.
a) What is the probability that a randomly selected employee will pass the psychologist's test?
b) What is the probability that an employee who doesn't pass the test will be rated excellent or satisfactory?
2. A Professor finds that he awards a final grade of A^{+} in QT to 20% of the students. Of those who obtain a final grade of A^{+}, 70% obtained an A^{+} in the mid-term examination. Also, 10% of the students who failed to obtain a final grade of A^{+} earned an A^{+} in the mid-term examination. What is the probability that a student with an A^{+} in the mid term examination will obtain a final grade of A^{+ } ?