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 24 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 2 defectives will be shipped? (b) What is the probability that a box containing only 1 defective will be sent back for screening? (a) The probability that a box containing 2 defectives will be shipped is (Round to four decimal places as needed.) (b) The probability that a box containing only 1 defective will be sent back for screening is (Round to four decimal places as needed.)

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### Probability in Quality Control Screening

A manufacturing company changes an acceptance scheme on items from a production line before they are shipped. An inspector takes one item at random from a box of 24 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 item, the entire box is sent back for 100% screening. If no defectives are found, the box is shipped.

#### Probability Questions:
(a) What is the probability that a box containing 2 defectives will be shipped?
(b) What is the probability that a box containing only 1 defective will be sent back for screening?

---

(a) The probability that a box containing 2 defectives will be shipped is _____.  
(Round to four decimal places as needed.)

(b) The probability that a box containing only 1 defective will be sent back for screening is _____.  
(Round to four decimal places as needed.)
Transcribed Image Text:### Probability in Quality Control Screening A manufacturing company changes an acceptance scheme on items from a production line before they are shipped. An inspector takes one item at random from a box of 24 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 item, the entire box is sent back for 100% screening. If no defectives are found, the box is shipped. #### Probability Questions: (a) What is the probability that a box containing 2 defectives will be shipped? (b) What is the probability that a box containing only 1 defective will be sent back for screening? --- (a) The probability that a box containing 2 defectives will be shipped is _____. (Round to four decimal places as needed.) (b) The probability that a box containing only 1 defective will be sent back for screening is _____. (Round to four decimal places as needed.)
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