This paper presents a novel approach for calculating a probabilistic worst-case response-time for messages in the Controller Area Network (CAN). CAN uses a bit-stuffing mechanism to exclude forbidden bit-patterns within a message frame. The added bits eliminate the forbidden patterns but cause an increase in frame length. How much the length is increased depends on the bit-pattern of the original message frame. Traditional response-time analysis methods assume that all frames have a worst-case number of stuff-bits. This introduces pessimism in the analysis. In this paper we introduce an analysis approach based on using probability distributions to model the number of stuff-bits. The new analysis additionally opens up for making trade-offs between reliability and timeliness, in the sense that the analysis will provide a certain probability for missing deadlines, which in the reliability analysis can be treated as a probability of failure. We evaluate the performance of our method using a subset of the SAE benchmark.