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Distance bounding protocols are an effective countermeasure against relay attacks including distance fraud, mafia fraud and terrorist fraud attacks. Reid et al. proposed the first symmetric key distance bounding protocol against mafia and terrorist fraud attacks . However,  claims that this is only achieved with a (7/8)n probability of success for mafia fraud, rather than the theoretical value of (3/4)n (for n rounds) achieved by distance bounding protocols without a final signature. We prove that the mafia fraud attack success using the Reid et al. protocol is bounded by (3/4)n and reduces as noise increases. The proof can be of further interest as it is the first - to the best of our knowledge - detailed analysis of the effects of communication errors on the security of a distance bounding protocol.