This paper is motivated by the fact that nearly half of U.S. college students drop out without earning a bachelor's degree. Its objective is to quantify how much uncertainty college entrants face about their graduation outcomes. To do so, we develop a quantitative model of college choice. The innovation is to model in detail how students progress towards a college degree. The model is calibrated using transcript and financial data. We find that more than half of college entrants can predict whether they will graduate with at least probability. As a result, stylized policies that insure students against the financial risks associated with uncertain graduation have little value for the majority of college entrants.