Picking an item in the presence of other objects can be challenging as it involves occlusions and partial views. Given object models, one approach is to perform object pose estimation and use the most likely candidate pose per object to pick the target without collisions. This approach, however, ignores the uncertainty of the perception process both regarding the target's and the surrounding objects' poses. This work proposes first a perception process for 6D pose estimation, which returns a discrete distribution of object poses in a scene. Then, an open-loop planning pipeline is proposed to return safe and effective solutions for moving a robotic arm to pick, which (a) minimizes the probability of collision with the obstructing objects; and (b) maximizes the probability of reaching the target item. The planning framework models the challenge as a stochastic variant of the Minimum Constraint Removal (MCR) problem. The effectiveness of the methodology is verified given both simulated and real data in different scenarios. The experiments demonstrate the importance of considering the uncertainty of the perception process in terms of safe execution. The results also show that the methodology is more effective than conservative MCR approaches, which avoid all possible object poses regardless of the reported uncertainty.