 Stochastic Interpretation: Consider the elements \(a\) and \(b\) of \(A\) to be actions, for example, pressing buttons on a machine. In this case, pressing a button does not have a certain outcome. For instance, if the machine is in state \(x\), there is a \(1/2\) probability it will remain in the same state after pressing \(a\), but a \(1/4\) probability of remaining in the same state after pressing \(b\). That is, 