Question: Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 99%

Components arriving at a distributor are checked for defects by two different inspectors (each component is checked by both inspectors). The first inspector detects 99% of all defectives that are present, and the second inspector does likewise. At least one inspector does not detect a defect on 2% of all defective components. What is the probability that the following occur?

(a)

A defective component will be detected only by the first inspector?

A defective component will be detected 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)?

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