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A manufacturing company changes an acceptance scheme on items from a production line before they are...

A manufacturing company changes an acceptance scheme on items from a production line before they are shipped. An inspector takes 1 item at random from a box of

25

​items, inspects​ it, and then replaces it in the​ box; a second inspector does likewise.​ Finally, a third inspector goes through the same procedure. If any of the three inspectors find a​ defective, the entire box is sent back for​ 100% screening. If no defectives are​ found, the box is shipped.

​(a) What is the probability that a box containing 4

defectives will be​ shipped?

​(b) What is the probability that a box containing only 1

defective will be sent back for​ screening?

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