Hybrid human/computer systems promise to greatly expand the usefulness of query processing by incorporating the crowd for data gathering and other tasks. Such systems raise many database system implementation questions. Perhaps most fundamental is that the closed world assumption underlying relational query semantics does not hold in such systems. As a consequence the meaning of even simple queries can be called into question. Furthermore query progress monitoring becomes difficult due to non-uniformities in the arrival of crowdsourced data and peculiarities of how people work in crowdsourcing systems. To address these issues, we develop statistical tools that enable users and systems developers to reason about tradeoffs between time/cost and completeness. These tools can also help drive query execution and crowdsourcing strategies. We evaluate our techniques using experiments on a popular crowdsourcing platform.