Taking the famous genetic toggle switch as an example, we numerically investigated the effect of noise on bistability. We found that extrinsic noise resulting from stochastic fluctuations in synthesis and degradation rates and from the environmental fluctuation in gene regulatory processes can induce coherent switch, and that there is an optimal noise intensity such that the noise not only can induce this switch, but also can amplify a weak input signal. In addition, we found that the intrinsic noise introduced through the Poisson τ-leap algorithm cannot induce such a switch.