In this paper a few "difficult" problems related to simultaneous stabilization of three plants (equivalent to a certain problem related to unit interpolation in H.) have been addressed through the framework of randomized algorithms. These problems which were proposed by Blondel (Simultaneous Stabilization of Linear Systems, Springer, Berlin, 1994) and Blondel and Gevers (Math. Control Signals Systems 6 (1994) 135) concern the existence of a controller.