The Belief-Desire-Intention (BDI) architecture is a popular framework for rational agents, yet most verification approaches are limited to analysing qualitative properties, for example whether an intention completes. BDI-based systems, however, operate in uncertain environments with dynamic behaviours: we may need quantitative analysis to establish properties such as the probability of eventually completing an intention. We define a probabilistic extension to the Conceptual Agent Notation (CAN) for BDI agents that supports probabilistic action outcomes, and probabilistic plan and intention selection. The semantics is executable via an encoding in Milner's bigraphs and the BigraphER tool. Quantitative analysis is conducted using PRISM. While the new semantics can be applied to any CAN program, we demonstrate the extension by comparing with standard plan and intention selection strategies (e.g. ordered or fixed schedules) and evaluating probabilistic action executions in a smart manufacturing scenario. The results show we can improve significantly the probability of intention completion, with appropriate probabilistic distribution. We also show the impact of probabilistic action outcomes can be marginal, even when the failure probabilities are large, due to the agent making smarter intention selection choices.