You've made the problem much harder . . .
Since the items are replaced, the probabilities are independent.
There are 3 Defective and 22 Good: .A company uses three-step testing scheme on items before they are shipped.
Boxes of 25 are readied for shipment.
An inspector takes one item at random, inspects it, then replaces it in the box.
A second inspector does the same. Finally, a third inspector does likewise.
If any defectives are found, the entire box is sent back.
If no defectives are found, the box is shipped.
(a) What is the probability that a box containing 3 defectives will be shipped?
The box will be shipped if each inspector draws a Good.
There is 1 Defective and 24 Good: .(b) What is the probability that a box containing only one defective will be sent back?
The box is sent back if at least one inspector finds a Defective.