We estimate the probability of detecting a gravitational wave signal from coalescing compact binaries in simulated data from a ground-based interferometer detector of gravitational radiation using Bayesian model selection. The simulated waveform of the chirp signal is assumed to be a spin-less Post-Newtonian (PN) waveform of a given expansion order, while the searching template is taken to be either of the same PN family as the simulated signal or one level below its PN expansion order. Within the Bayesian framework we estimate the detection probabilities and the statistical uncertainties due to noise as a function of the signal-to-noise ratio (SNR), and the posterior distributions of the parameters characterizing the chirp signal. Our analysis indicates that the detection probabilities are not compromised when simplified models are used, while the accuracies in the determination of the parameters can be significantly worsened.