  We develop an approach where the quantum system states and quantum
observables are described as in classical statistical mechanics -- the states
are identified with probability distributions and observables, with random
variables. An example of the spin-1/2 state is considered. We show that the
triada of Malevich's squares can be used to illustrate the qubit state. We
formulate the superposition principle of quantum states in terms of
probabilities determining the quantum states. New formulas for nonlinear
addition rules of probabilities providing the probabilities associated with the
interference of quantum states are obtained. The evolution equation for quantum
states is given in the form of a kinetic equation for the probability
distribution identified with the state.
