What is the underlying mathematics behind law of mass action? When calculating reaction rates of of a chemical reaction, what is the reason taking product of concentration of chemicals (i. e. V+ = k[A][B]) instead addition (e.g. k[A] + k[B])?
Does this related to probability or which rule of derivation explains this?


Probability is indeed one way to view this. Consider 2 independent chemicals A,B who react when they are at the same place at the same time. Assuming the distribution is homogeneous and independent, the probability of a certain molecule of type $A$ to be at a given position $x$ is the density $[A]$ times the volume $dx$, so the probability of both materials to react is proportional to $[A][B]$, as the events are independent. The 'orders' come from reactions when several molecules of each chemical are needed simultaneously, eg $2A+B\rightarrow [A]^2[B]$ since we need the probability of 2 molecules of $A$ to arrive independently for the interaction to occur.
