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A new approach for the computation of probability distributions for coupled first order chemical reactions is introduced. The approach is based on system theory, where the system states are chemical species and the signals are probabilities. We derive the transfer functions of the so defined systems and show that they can be applied to various reaction environments. The use of block diagrams offers a clear, visual, and convenient way to decompose a complicated reaction system into simpler sub-systems and vice versa. Since the state of the system is defined as a molecule species instead of molecule population, with this method, one can study chemical reactions involving any number of molecules.