This paper proposes to develop a latent class risky choice for interurban mode choice that we apply to SP data that were collected in the French Rhône-Alpes region. Risk is related to travel time outcomes, where its considered that travelers may arrive on-time or late with some delay probability. We here integrate variety of attitudes to probabilities and attitudes to risky outcomes within the rank-dependent utility (RDU) framework, leaving up divergence from the latter (i.e. choice of a decision-making framework) for further research. We assume that all decision-makers behave following that theoretical framework yet considering that they may have different attitudes to risk, e.g. attitudes to probabilities and attitudes to outcomes of the risky prospect. It offers enough flexibility to characterize unobserved behavioral clusters in a sample of observed travel choices. It makes possible to elegantly consider from risky-prone behaviors to risk-adverse behaviors with risk-neutral behaviors as a balancing point in a theoretically consistent way.