As private information of individuals become more accessible, data privacy evolved to be an important aspect of communication technologies. Among existing privacy definitions, the utility privacy trade-off model is suitable for the assessment of privacy due to its relation with the information theory and the rate distortion theory. In this paper, the effects of the transmission errors due to the wireless channel are studied with respect to the utility privacy trade-off in a wireless communication network. First, the transmission error probability is embedded to the existing trade-off definitions. Then, it is shown via numerical examples that binary and normal distributed sources comply with the limits that are set by the updated rate distortion equivocation and equivocation distortion functions.