Decarbonization policies have significantly increased the adoption of plug-in electric vehicles (PEVs) worldwide. This paper develops and applies a probabilistic method for assessing large-scale integration of PEVs in a real low voltage distribution system (DS) in Stockholm County, Sweden. The framework employs Monte Carlo simulations to capture uncertainties in driver behaviors, daily distances, charging start times, and vehicle allocation. Its key contributions are: (i) a replicable data-driven Monte Carlo framework that merges DS operator (DSO) load data with travel habit statistics, (ii) realistic charging-profile generation, (iii) demonstrate that adding price signals plus a network constraint almost doubles hosting capacity and cuts user costs, and (iv) a systematic comparison of uncontrolled versus controlled charging that clarifies technical-economic trade-offs. The analysis considers PEV penetration levels (Pls)—defined as the percentage of customer units (CUs) with a PEV among all CUs with permanent access to a passenger vehicle—up to 100 %. Key performance indicators, analyzed at the 95th percentile to represent near-worst-case outcomes, include voltage profiles, transformer and line loading, aggregated peak power, technical losses, and hosting capacity. Uncontrolled charging raises peak demand, causing voltage and overload violations that cap hosting capacity at Pl 27 %. Adding price signals with a peak demand cap lifts capacity to Pl 49 %, halves overloads, and lowers charging costs by about 10 %. Night-time charging suffices up to Pl 49 %; above Pl 75 %, morning charging is needed to keep power quality within limits. The method is broadly replicable and offers actionable guidance for municipalities, DSOs, and policymakers seeking to ensure a sustainable and cost-effective transition toward electrified transportation while maintaining reliable DS operation.