Human health risk assessment (HHRA) in probabilistic space is an ongoing research activity that plays a crucial role in managing water quality risks. This study formulates a probabilistic HHRA based on two-dimensional Monte Carlo simulation (MCS) for a set of groundwater samples exposed to trace elements of arsenic (As), nickel (Ni), and lead (Pb) for dermal and oral pathways. The developed two-dimensional MCS captures the parameter variability in Dimension I and the functional uncertainty of the probability functions in Dimension II. The probabilistic HHRA was implemented in the Tabriz plain, a strategic aquifer in northwest Iran. The results of probabilistic HHRA indicate that the minimum and maximum values for total risk are 10 and 44 times greater than the tolerable contamination range (TCR = 1 × 10−4), respectively. The HHRA results also delineate the hotspots in the aquifer for individual and total designated elements. The results also indicate that remedial strategies are necessary for As and Ni as their exposure values at the 95th percentile exceed the TCL. We also used the correlation coefficient matrix and the factor analysis to detect the probable sources of the designated trace elements. The results show that As and Pb are likely to have geogenic sources. Our findings also suggest that geogenic and anthropogenic sources contribute to Ni concentration in the aquifer. These findings support the decision to protect the public health of the over 1.7 Million people who use groundwater resources for drinking.