Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 90% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 20% of all defective components. What is the probability that the following occur?
a. A defective component will be detected only by the first inspector? By exactly one of the two inspectors?
b. All three defective components in a batch escape detection by both inspectors (assuming inspections of different components are independent of one another)?