This paper presents a probabilistic formulation of unsaturated flow through rough multi-segmented fractures, with emphasis on Dripping Initiation Time (DIT), and attempts to explain the fast flow paths detected at the Yucca Mountain (YM) Exploratory Studies Facility (ESF). Three scenarios of parameters were used to test the validity of the model with these fast flow paths. The scenarios differed in the DITs and the corresponding parameter configurations were also tested for three different stratigraphic horizon depths. Each depth represented a different location where fast flow has been detected at YM. The first depth corresponds to the Bow Ridge Fault; the second represents a network of steep fractures and cooling joints with large variability in dip; and the third location, probably connected to the Diabolous Ridge Fault, has a flow path that is low dipping. Monte Carlo simulations for each configuration and depth produced probabilistic results from nine scenarios for DITs, which are quite consistent with field observations.