We investigate the use of probabilistic models and cost-benefit analyses to guide the operation of a Web-based question-answering system. We first provide an overview of research on question answering systems. Then, we present details about AskMSR, a prototype question-answering system that synthesizes answers from the results of queries to a Web search engine. We describe Bayesian analyses of the quality of answers generated by the system and show how we can endow the system with the ability to make decisions about the nature and number of queries that should be issued, by considering the expected value and cost of submitting the queries. Finally, we review the results of a set of experiments.