A probabilistic description of a macroscopic system is introduced taking into account the myriad of microstates that are compatible with a given microstate. An equilibrium state is identified as a state that may be obtained through a maximal number of microscopic states. This criterium leads to several single-particle distributions, such as the classical Maxwell-Boltzmann distribution and quantum distributions such as the Bose-Einstein, Planck, and Fermi-Dirac distributions. The connection between thermodynamics and the statistical description is established. The statistical description of a gas is carried out in some detail with the conclusion that the thermodynamic quantities may be seen as resulting from statistical averages over the microscopic particles. It is emphasized that the statistical microscopic description in general requires a semiclassical treatment, in the sense that some properties associated with quantum phenomena, like the Heisenberg uncertainty relation and/or the Pauli exclusion principle, have to be introduced, as the solution of the Gibbs paradox shows.