Ambiguities and unstated assumptions in probabilistic reasoning.

Ostensibly simple probabilistic reasoning problems are sometimes surprisingly difficult. One source of difficulty is the omission from a problem description of information essential to an unambiguous understanding of the situation. When this is so, assumptions must be made to permit the computation of probabilities. Different assumptions lead to different conclusions, and if the assumptions are not stated, disagreements regarding problem solutions can occur, even among experts. The author reviews several such problems and their treatment in the literature. He proposes accounts of why problems can be difficult even when not ambiguous and discusses some approaches that can make solutions easier to find or understand.