In: Statistics and Probability
A manufacturing company uses an acceptance scheme on items from a production line before they are shipped. Boxes of 20 items are readied for shipment. An inspector takes one item at random, inspects it, and then replaces it in the box; the next 8 inspectors do likewise. Finally, a tenth inspector goes through the same procedure.
Find the probability that 3 inspectors find defective in the box containing 2 defectives. (Round from the fifth decimal place to the fourth decimal place.)
[Hint: Think about the random variable, X representing the number of inspectors that found defective.]