The article introduces the basic ideas and investigates the probabilistic version of rough set theory. It relies on both classification knowledge and probabilistic knowledge in analysis of rules and attributes. One-way and two-way inter-set dependency measures are proposed and adopted to probabilistic rule evaluation. A probabilistic dependency measure for attributes is also proposed and demonstrated to have the monotonicity property. This property makes it possible for the measure to be used to optimize and evaluate attribute based-representation through computation of attribute reduct, core and significance factors.