Confidence is central to safety and assurance cases: how much confidence a decision requires and how much the argument actually provides are both important questions. We present a new method for assessing probabilistic confidence in assurance case arguments that is simple, systematic and sound. It exploits the ways claims are decomposed in a structured argument and provides different approaches according to the different degrees of (in)dependence and diversity among subclaims and the way they eliminate concerns that undermine confidence in their parent claims. The method uses only elementary probabilistic constructions that are well-known in other contexts (e.g., Frechet bounds) but we interpret and apply them in a manner that is specifically focused on assurance arguments and requires no background in probabilistic analysis. We show that the method is not susceptible to the counterexamples that Graydon and Holloway exhibit for other approaches to confidence and we recommend it as an additional tool in evaluation of Assurance 2.0 arguments. The primary evaluation criteria for Assurance 2.0 remain logical indefeasibility and dialectical examination, but probabilistic assessment can be useful in evaluating cost/confidence tradeoffs for different risk levels, and the overall balance of confidence across a structured argument.