In multi-agent environments, effective interaction hinges on understanding the beliefs and intentions of other agents. While prior work on goal recognition has largely treated the observer as a passive reasoner, Active Goal Recognition (AGR) focuses on strategically gathering information to reduce uncertainty. We adopt a probabilistic framework for Active Goal Recognition and propose an integrated solution that combines a joint belief update mechanism with a Monte Carlo Tree Search (MCTS) algorithm, allowing the observer to plan efficiently and infer the actor's hidden goal without requiring domain-specific knowledge. Through comprehensive empirical evaluation in a grid-based domain, we show that our joint belief update significantly outperforms passive goal recognition, and that our domain-independent MCTS performs comparably to our strong domain-specific greedy baseline. These results establish our solution as a practical and robust framework for goal inference, advancing the field toward more interactive and adaptive multi-agent systems.