Resource-bounded alternating-time temporal logic (RB-ATL), an extension of Coalition Logic (CL) and Alternating-time Temporal Logic (ATL), allows reasoning about resource requirements of coalitions in concurrent systems. However, many real-world systems are inherently probabilistic as well as resource-bounded, and there is no straightforward way of reasoning about their unpredictable behaviours. In this paper, we propose a logic for reasoning about coalitional power under resource constraints in the probabilistic setting. We extend RB-ATL with probabilistic reasoning and provide a standard algorithm for the model-checking problem of the resulting logic Probabilistic Resource-Bounded ATL (pRB-ATL).