Yes, it's possible. Basically, have a script on the door so when you activate it, the script will run.
pseudo code:
scn randomdoorscript int iRanNum Begin OnActivate Player set iRanNum to GetRandomPercent ;Not sure of the actual function name if iRanNum < 26 Player.MoveTo RoomARef ;I use a persistent x-marker with the name RoomARef in the spot you want the player to be elseif iRanNum < 51 Player.MoveTo RoomBRef ;another x-marker, as persistent with the name RoomBRef elseif iRanNum < 76 Player.MoveTo RoomCRef elseif iRanNum < 101 Player.MoveTo RoomDRef endif End
Something like that would do what you wanted. Hope that helps, good luck.
-Mush-