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The goal of this work is to forecast human activities that may require robot assistance. Each activity consists of consecutive actions. Each action is bounded by initial and final state and is created by the motion trajectory. The states are defined in the training phase. The vision and depth sensors are used for data collection. The data are processed and the structured database is built. This base is used for making prediction. The method allows us to forecast the trajectories of nominally possible motion goals (prognosing of an action). The probability functions support the selection of possible motion goal. Then the possible motion trajectory is created which predicts the ongoing action. The activity is predicted on the basis of already completed action sequences and using knowledge about possible sequences stored in the database. The core of the reasoning process are: the probability functions, the action graphs (describing the activities) and the structured database. The approach was evaluated using four datasets: CAD 60, CAD-120, WUT-17, and WUT-18. The efficiency of the presented solution compared to the other existing state-of-the-art methods is also investigated.