Rivin and Maher independently proved that a non-elementary random walk on the mapping class group gives rise to a pseudo-Anosov in asymptotic probability one. Their approaches utilize the symplectic representation of the mapping class group or the action on the curve complex, respectively. In this talk, I will describe another approach that relies on the Teichmüller geometry, namely, Bers' proof of Nielsen-Thurston's
classification and the contracting property of thick Teichmüller geodesics.