The study reported in the present paper is part of a larger project, which aims to explore possibilities and challenges in developing a teaching practice that supports students’ ability to model random dependent situations by a Bayesian approach. A central premise is that modeling should be based on situations that appear realistic to the students. Given this premise, the specific purpose of the present study is to identify and characterize uncertain situations that are realistic and suitable for a Bayesian treatment. The study involves reviewing some of the literature related to Bayesian applications. Based on that review we distinguish detecting (test) situations and construction composition situations as two general types of Bayesian modeling situations.