The random walk method is applied to a one-dimensional Helmholtz equation with a variable wave number. The solution is represented as a mathematical expectation of a specified functional on paths in a complex space. This solution degenerates to the ray-method approximation in domains where the latter method may be used, but the probabilistic formulas presented describe also backscattered waves whose existence is not explained by the standard asymptotic techniques. The numerical results confirm the efficiency of the random walk approach to the analysis of wave propagation.