Summary: We present an analytic investigation of the mean first passage time in two opposite directions (from the left well to the right well and from right to left) by studying symmetrical bistable systems driven by correlated Gaussian white noises, and prove that the mean first passage time in two opposite directions is not symmetrical any more when noises are correlated. As examples, the mean first passage time in the quartic bistable model and the sawtooth bistable model are calculated, respectively. From the analytic results of the mean first passage time, we testify further the relation \(T\)(from \(x_-\) to \(x_+,\lambda)\neq T\)(from \(x_+\) to \(x_-,\lambda)\) in the same area of the parameter plan. Moreover, it is found that the dependences of \(T^+\) (i.e., \(T\)(from \(x_-\) to \(x_+,\lambda))\) and \(T^-\) (i.e., \(T\)(from \(x_+\) to \(x_-,\lambda))\) upon the multiplicative noise intensity \(Q\) and the additive noise intensity \(D\) exhibit entirely different properties. For the same areas of the parameter plan: in the quartic bistable system, when the \(T^+\) vs. \(Q\) curve exhibits a maximum, while the \(T^-\) vs. \(Q\) curve is monotonous; when the \(T^+\) vs. \(D\) curve is monotonous, while the \(T^-\) vs. \(D\) curve experiences a phase transition from decreasing monotonously to possessing one minimum. Increasing \(Q\), when the \(T^+\) vs. \(D\) curve experiences a phase transition from decreasing monotonously to possessing one maximum, while the \(T^-\) vs. \(D\) curve only increases monotonously. Similar behaviour also exist in the sawtooth bistable model.