Approximate adders are used in applications that are error tolerant to save on power and area. We consider the class of two-part segmented approximate adders, where the upper part of the sum is computed accurately and the lower part of the sum is approximated. In this paper, we model the error of various two-part segmented approximate adders using probabilistic analysis and derive expressions for some basic error metrics used in literature. We compare the results obtained using our expressions for various error metrics with those using Monte Carlo simulations for different input distributions. Further, in an image addition application, we use our expression derived for mean square error and show that it predicts the PSNR correctly. © 2018 IEEE.