Administrative problems such as computer malfunction and power outage occasionally lead to missing item scores and hence to incomplete data on mastery tests such as the AP and U.S. Medical Licensing examinations. Investigators are often interested in estimating the probabilities of passing of the examinees with incomplete data on mastery tests. However, there is a lack of research on this estimation problem. The goal of this article is to suggest two new approaches--one each based on classical test theory and item response theory--for estimating the probabilities of passing of the examinees with incomplete data on mastery tests. The two approaches are demonstrated to have high accuracy and negligible misclassification rates.