In fault-tolerant computing, dependability of systems is usually demonstrated by abstracting from failure probabilities (under simplifying assumptions on failure occurences). In the specification framework FOCUS, we show under which conditions and to which extent this is sound: We use a specification language that is interpreted in the usual abstract model and in a probabilistic model. We give probability bounds showing the degree of faithfulness of the abstract model wrt the probabilistic one. These include cases where the usual assumptions are not fulfilled.