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)?

Answer Step 1 of 3 P(both detect the defect)=1-P(at least one doesn’t detect) =1-0.2=0.8 Step 2 of 3 a)P(1st detect 2nd doesn’t detect)=P(1st detect)-P(1st detect 2nd detect) =0.9-0.8=0.1 Similarly P(1st doesn’t detect 2nd detect)=0.1 P(exactly one does)=0.1+0.1=0.2