Components arriving at the distributor are checked for defects by two different inspectors (each component is checked by a 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% off all defective component. What is the probability that the following occur?

a. A defective components will be detected only by the first inspector? By exactly one of 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)?

Show me a vann diagram and all the necessary steps and details from scratch as much as possible please. Thank you.