We introduce a simplified stochastic model for the A+B-2 surface reaction with diffusion of the monomer particle. We use a stochastic description which consists only of an autonomous differential equation system with four variables (the coverage of A and B and the corresponding pairs). The solution of this system is a straightforward process. We compare the values of the phase transition points with a much more complex stochastic ansatz which has been introduced earlier [Mai, Kuzovkov, and von Niessen, J. Chem; Phys. 100, 6073 (1994)]. We find good agreement in the prediction of the first-order phase transition with the complete treatment. The ansatz also gives the second-order transition, but the results are not quantitative in the neighborhood of the second-order phase transition.