Multi-stage serverless applications, i.e., workflows with many computation and I/O stages, are becoming increasingly representative of FaaS platforms. Despite their advantages in terms of fine-grained scalability and modular development, these applications are subject to suboptimal performance, resource inefficiency, and high costs to a larger degree than previous simple serverless functions. We present Aquatope, a QoS-and-uncertainty-aware resource scheduler for end-to-end serverless workflows that takes into account the inherent uncertainty present in FaaS platforms, and improves performance predictability and resource efficiency. Aquatope uses a set of scalable and validated Bayesian models to create pre-warmed containers ahead of function invocations, and to allocate appropriate resources at function granularity to meet a complex workflow's end-to-end QoS, while minimizing resource cost. Across a diverse set of analytics and interactive multi-stage serverless workloads, Aquatope significantly outperforms prior systems, reducing QoS violations by 5x, and cost by 34% on average and up to 52% compared to other QoS-meeting methods.