The concept of probability is not an easy concept for high school and college students to understand. This paper identifies and analyzes the students' alternative frameworks from the viewpoint of constructivism. There are various interpretations of probability through mathematical history: classical, frequentist, and subjectivist interpretation. These interpretations provide a context for evaluating various beliefs about probability held by students long before the start of formal instruction. The study develops an outcome approach model of informal reasoning under certainty and presents a few excerpts from conversations with students about probability to demonstrate how statements can be understood according to the outcome approach. Three kinds of students' reasoning statements are discussed: confusing statements, statements that sound incorrect, and statements which contain two conflicting views. This study suggests three general types of criteria against which students are encouraged to evaluate their current beliefs. These are the fit between their beliefs and: (1) the beliefs of others; (2) their other, related beliefs; and (3) empirical observations. (YP)