This paper exemplifies the application of U.S. Environmental Protection Agency's water quality model, QUAL2E-UNCAS in assessing the pollution risk of a tropical river. The rivers selected for study were Hindon (main river) and Kali (its tributary) flowing through Uttar Pradesh district of Northern India. The model application to the two rivers revealed poor water quality in terms of dissolved oxygen (DO), biochemical oxygen demand (BOD), and ammonia concentrations. Monte Carlo simulations were performed on two different data sets that were confirming to marked seasonal variations. The Monte Carlo simulation (MCS) derived 95% confidence level for these parameters strengthened the fact that all point sources were exploiting the assimilative capacity of the two rivers. In order to ascertain probabilistically the risk at which two rivers were falling short of desired water quality, probability curves based on effluent standards and available water quality were prepared. On mapping the two curves, it was found that at 95% probability, Hindon River was flowing with 53 to 100% less of desired DO, up to 100% more of minimum BOD, and probability with which ammonia concentration would not be more than the desired concentration was found to fall downstream. The Kali headwaters showed better quality during low river temperature but worsened downstream with up to 100% violation in all the above observed parameters. It is expected that similar studies wherein the dependable levels with which a polluted river can be understood to fall short of desired water quality can prove to be useful in ascertaining the efficacy of effluent standards and/or follow-up of pollution control measures.