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Safety cases capture a structured argument linking claims about the safety of a system to the evidence justifying those claims. However, arguments in safety cases tend to be predominantly qualitative. Partly, this is attributed to the lack of sufficient design and operational data necessary to measure the achievement of high-dependability goals, particularly for safety-critical functions implemented in software. The subjective nature of many forms of evidence, such as expert judgment and process maturity, also contributes to the overwhelming dependence on qualitative arguments. However, where data for quantitative measurements can be systematically collected, quantitative arguments provide benefits over qualitative arguments in assessing confidence in the safety case. In this paper, we propose a basis for developing and evaluating the confidence in integrated qualitative and quantitative safety arguments. We specify a safety argument using the Goal Structuring Notation (GSN), identify and quantify uncertainties therein, and use Bayesian Networks (BNs) as a means to reason about confidence in a probabilistic way. We illustrate our approach using a fragment of a safety case for an unmanned aircraft system (UAS).