The stochastic resonance (SR) for a stochastic bistable system driven by a dichotomous noise and a periodic signal as well as by additive white noise is considered from the view of signal-to-noise ratio (SNR). It is found that the SNR appears SR behavior when it is plotted as a function of the strengths of the noises and as a function of the parameters of the stochastic potential. The influence of the correlation rate of the dichotomous noise on the SNR is studied.