Question

A manufacturing company uses an acceptance
scheme on items from a production line before they
are shipped. The plan is a two-stage one. Boxes of 25
items are readied for shipment, and a sample of 3 items
is tested for defectives. If any defectives are found, 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 3
defectives will be shipped?

(b) What is the probability that a box containing only
1 defective will be sent back for screening?