This study proposes a methodology to analyze the impacts of Electric Vehicles (EVs) on Low Voltage (LV) distribution networks based on probabilistic models developed for the charging process of EVs. In addition to the battery charging characteristics, Gaussian distribution function for EV plug-in times and Weibull distribution function for daily travel times are utilized in simulations. Monte Carlo based load flow simulations are performed in order to evaluate the response of the LV networks to various EV and load scenarios and different multi-tariff mechanisms. The sample networks are investigated for branch overloads, excessive voltage drops and losses using a systematic reporting approach developed. This method guides the utilities to determine the necessary investments on LV networks and their associated time frames. The expected consumer reaction to different multi tariff systems can also be modeled to assess the economic feasibility of a new multi tariff system against necessary investments in the LV network.