Problem-Based Learning (PBL) is a popular approach to instruction that supports students to get hands-on training by solving problems. Question Pool websites (QPs) such as LeetCode, Code Chef, and Math Playground help PBL by supplying authentic, diverse, and contextualized questions to students. Nonetheless, empirical findings suggest that 40% to 80% of students registered in QPs drop out in less than two months. This research is the first attempt to understand and predict student dropouts from QPs via exploiting students engagement moods. Adopting a data-driven approach, we identify five different engagement moods for QP students, which are namely challenge-seeker, subject-seeker, interest-seeker, joy-seeker, and non-seeker. We find that students have collective preferences for answering questions in each engagement mood, and deviation from those preferences increases their probability of dropping out significantly. Last but not least, this paper contributes by introducing a new hybrid machine learning model (we call Dropout-Plus) for predicting student dropouts in QPs. The test results on a popular QP in China, with nearly 10K students, show that Dropout-Plus can exceed the rival algorithms dropout prediction performance in terms of accuracy, F1-measure, and AUC. We wrap up our work by giving some design suggestions to QP managers and online learning professionals to reduce their student dropouts.