Movement prioritization is a common approach to combine controllers of different tasks for redundant robots,where each task is assigned a priority. The priorities of the tasks are often hand-tuned or the result of an optimization,but seldomly learned from data. This paper combines Bayesian task prioritization with probabilistic movement primitives to prioritize full motion sequences that are learned from demonstrations. Probabilistic movement primitives (ProMPs) can encode distributions of movements over full motion sequences and provide control laws to exactly follow these distributions.The probabilistic formulation allows for a natural application of Bayesian task prioritization. We extend the ProMP controllers with an additional feedback component that accounts inaccuracies in following the distribution and allows for a more robust prioritization of primitives. We demonstrate how the task priorities can be obtained from imitation learning and how different primitives can be combined to solve even unseen task-combinations. Due to the prioritization, our approach can efficiently learn a combination of tasks without requiring individual models per task combination. Further, our approach can adapt an existing primitive library by prioritizing additional controllers, for example, for implementing obstacle avoidance.Hence, the need of retraining the whole library is avoided in many cases. We evaluate our approach on reaching movements under constraints with redundant simulated planar robots and two physical robot platforms, the humanoid robot “iCub” and a KUKA LWR robot arm.