At the Educational Testing Service, the K-Index is used to assess unusual agreement between the incorrect responses of two test takers on a multiple-choice test. Since the fall of 1996, the value of the K-Index used for this assessment has been suggested, based on the Bonferroni inequality. The resulting value is referred to as a Probability of Matching Incorrect Responses (PMIR). If a test taker copies from someone (a Source) with no incorrect responses, the PMIR is useless (i.e., has zero power) for detecting unusual agreement. Similarly, if a Source has relatively few incorrect responses, the power of the PMIR will be low. We propose a framework within which to study the power of the PMIR. The power function derived within this framework exhibits quite complex behavior; however, we concluded that the power of the PMIR to detect substantial amount of unit is quite low, even when the Source has relatively large number of incorrect responses.