Large language models (LLMs) are increasingly adopted in high-stakes domains such as healthcare and medical education, where the risk of generating factually incorrect (i.e., hallucinated) information is a major concern. While significant efforts have been made to detect and mitigate such hallucinations, predicting whether an LLM's response is correct remains a critical yet underexplored problem. This study investigates the feasibility of predicting correctness by analyzing a general-purpose model (GPT-4o) and a reasoning-centric model (OSS-120B) on a multiple-choice prosthodontics exam. We utilize metadata and hallucination signals across three distinct prompting strategies to build a correctness predictor for each (model, prompting) pair. Our findings demonstrate that this metadata-based approach can improve accuracy by up to +7.14% and achieve a precision of 83.12% over a baseline that assumes all answers are correct. We further show that while actual hallucination is a strong indicator of incorrectness, metadata signals alone are not reliable predictors of hallucination. Finally, we reveal that prompting strategies, despite not affecting overall accuracy, significantly alter th