In the example in Section 5.9, consider the probability that three items have mismatched labels and one of these items is found.

a. Calculate the probability that all three items would pass inspection and, therefore, there would be two additional ones out of the 84 remaining in the field.

b. Calculate the probability that exactly one of the two remaining items with mismatched labels is among the 84 items still in the field. (Hint: Add together two probabilities, namely the probability that exactly one item is removed at the second stage but none at the third, added to the probability that exactly one item is removed at the third stage but none at the second).

c. Use the results from

(a) and

(b) above to calculate the probability that at least one of the two additional items with mismatched labels is among the 84 remaining in the field.

d. Based on the result in (c), do you think the probability is small enough not to recall the 84 items for inspection?