A business process is a set of structured activities that provide a certain service or product. Business processes can be modeled using the BPMN standard, and several industrial platforms have been developed for supporting their design, modeling, and simulation. This paper presents a rewriting logic executable specification of BPMN with time and extended with probabilities. Duration times and delays for tasks and flows can be specified as stochastic expressions, while probabilities are associated to various forms of branching behavior in gateways. These quantities enable discrete-event simulation and automatic stochastic verification of properties such as expected processing time, expected synchronization time at merge gateways, and domain-specific quantitative assertions. The mechanization of the stochastic analysis tasks is done with Maude's statistical model checker PVeStA. The approach is illustrated with a running example and further experimental results encompass specifications from the literature.