A. If the probability of improper operations "X" is .29, the investigation is not expected to be cost beneficial. Therefore, Bagley would not be indifferent.

B. If the probability of improper operation "X" is 0.60, investigation is expected to be cost beneficial. Therefore, Bagley would not be indifferent.

C. If the probability of improper operation "X" is 0.71, investigation is expected to be cost beneficial. Therefore, Bagley would not be indifferent.

D. In order to determine this percentage, we must determine at what percentage of likelihood of error the expected cost of the investigation is equal to the expected cost of not investigating. In case of investigation, total costs will be equal to the sum of the cost of investigation itself ($6,000) and the expected cost of correction ($18,000X), where "X" is the probability of improper operations. The expected cost of not doing an investigation is $33,000X. Equating both sides would allow us to find X.

Our equation is:

33,000X = 6,000 + 18,000X.

To solve for X,

(1) Subtract 18,000X from both sides of the equation:

15,000X = 6,000

 (2) Divide both sides of the equation by 15,000:

X = .40

If the probability of an improper operation is 40%, Bagley is indifferent as to whether or not he investigate.