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Applied Engineering through Cost Benefit Analysis and Bayesian Analysis of Stochastic Risk Assessment for Mining Waste Management contributes positively to the development of an innovative methodology that could be implemented on an industrial scale. The current study examines the techno-economic sustainability of two potential options (scenarios) that a start-up gold mining company may select for the disposal of tailings for the same mining site. First, scenario A(0) refers to mining activities without implementing legal obligations that express the policy of Circular Economy and are mandatory in the mining industry. This scenario reflects the absence of the 3R's policy (reduce, recover, reuse wastes) and the non-implementation of environmental protection measures. In contrast, scenario A(1) involves mining activities with full implementation of environmental protection requirements by investing in metal recovery through a closed system of industrial units and avoiding tailings' free disposal to soil areas. Scenario A(1) aligns with the principles of the Circular Economy by minimizing the mass of hazardous tailings, enhancing recovery for beneficial materials contained in mining wastes, and increasing the potential utilization of recovered metals in separated industrial applications. The total cost for each case scenario depends on a) the project's nature of work, b) legislative requirements for environmental protection, and c) escalation of penalty cost for non-compliance with the corresponding legislation. Cost benefit analysis (CBA) evaluates the sustainability of each case scenario by its Financial Risk. The scope of this paper is to ensure the adaptability of the CBA appraisal tool to each similar subject of study, in which the lowest Financial Risk Indices characterize optimal business decisions. CBA's evaluation involves converting the parameters of each case scenario into monetary terms. CBA's extracted results are calibrated through Stochastic Risk Analysis-Assessment (SRA) to provide a more accurate Financial Risk (FR) estimation considering the escalation of Bayesian risk probability that describes the rate of total conformance in each examined case. Thus, both CBA and SRA have significant applications in actual conditions. The Financial Risk Assessment supported by CBA and SRA detects a high grade of economic sustainability for scenario A(1) compared to scenario A(0). A combined techno-economic analysis is provided by employing CBA considering the relevant legal obligations and technical parameters expressed in monetary terms. Simultaneously, the SRA considers CBA's output to calculate the grade of financial risk. The combination of CBA and SRA could be applied to similar projects, especially in waste management, to investigate their total grade of sustainability. [ABSTRACT FROM AUTHOR]