As video-streaming services have expanded and improved, cloud-based video has evolved into a necessary feature of any successful business for reaching internal and external audiences. In this paper, video streaming over distributed storage is considered where the video segments are encoded using an erasure code for better reliability. There are multiple parallel streams between each server and the edge router. For each client request, we need to determine the subset of servers to get the data, as well as one of the parallel stream from each chosen server. In order to have this scheduling, this paper proposes a two-stage probabilistic scheduling. The selection of video quality is also chosen with a certain probability distribution. With these parameters, the playback time of video segments is determined by characterizing the download time of each coded chunk for each video segment. Using the playback times, a bound on the moment generating function of the stall duration is used to bound the mean stall duration. Based on this, we formulate an optimization problem to jointly optimize the convex combination of mean stall duration and average video quality for all requests, where the two-stage probabilistic scheduling, probabilistic video quality selection, bandwidth split among parallel streams, and auxiliary bound parameters can be chosen. This non-convex problem is solved using an efficient iterative algorithm. Evaluation results show significant improvement in QoE metrics for cloud-based video as compared to the considered baselines.