Most formal methods see the correctness of a software system as a binary decision. However, proving the correctness of complex systems completely is difficult because they are composed of multiple components, usage scenarios, and environments. We present QuAC, a modular approach for quantifying the correctness of service-oriented software systems by combining software architecture modeling with deductive verification. Our approach is based on a model of the service-oriented architecture and the probabilistic usage scenarios of the system. The correctness of a single service is approximated by a coverage region, which is a formula describing which inputs for that service are proven to not lead to an erroneous execution. The coverage regions can be determined by a combination of various analyses, e.g., formal verification, expert estimations, or testing. The coverage regions and the software model are then combined into a probabilistic program. From this, we can compute the probability that under a given usage profile no service is called outside its coverage region. If the coverage region is large enough, then instead of attempting to get 100% coverage, which may be prohibitively expensive, run-time verification or testing approaches may be used to deal with inputs outside the coverage region. We also present an implementation of QuAC for Java using the modeling tool Palladio and the deductive verification tool KeY. We demonstrate its usability by applying it to a software simulation of an energy system.