This paper uses “revealed probability trade-offs” to provide a natural foundation for probability weighting in the famous von Neumann and Morgenstern axiomatic set-up for expected utility. In particular, it shows that a rank-dependent preference functional is obtained in this set-up when the independence axiom is weakened to stochastic dominance and a probability trade-off consistency condition. In contrast with the existing axiomatizations of rank-dependent utility, the resulting axioms allow for complete flexibility regarding the outcome space. Consequently, a parameter-free test/elicitation of rank-dependent utility becomes possible. The probability-oriented approach of this paper also provides theoretical foundations for probabilistic attitudes towards risk. It is shown that the preference conditions that characterize the shape of the probability weighting function can be derived from simple probability trade-off conditions.