The use of breathalysers to determine whether a person is 'Driving Under the Influence' (DUI) is an example of situations in which the outcome of a test - positive or negative - is used to determine whether a condition exists. As such, it is susceptible to a fallacy that is inherent in such situations: confusing the chances that a person would test positive if he/she was DUI with the chances that a person was DUI if he/she tested positive. This is referred to here as the breathalyser fallacy and this article provides quantitative estimates of the size of this fallacy. Almost all of the criticism of the conclusions of breathalyser tests (namely, a person over the limit is DUI, a person below the limit is not) concerns the likelihood of a person who is not DUI being incorrectly identified. This analysis questions this argument. We show that the likelihood of an innocent person testing positive depends on two further factors: (i) the a priori likelihood that a person selected for breath analysis is, in fact, DUI and (ii) the reliability of the test in terms of the likelihood of a DUI person being found to be over the limit. If these two likelihoods are high, then the probability of a person being guilty of DUI for a positive outcome on the breathalyser test would also be high, even though there is a significant chance that a person who is not DUI will be incorrectly identified as being over the limit.