The German RPG The Dark Eye handles things that way - combat actions are solved with a realtively simple, D20-roll under system, while skill tests are used with 3 d20, compared to three stats. However, last time I checked, that was a big, very cumbersome system with a lot of moving parts, options and modifiers.
The much more important question is: do players need to know? If transparancy of success rate is relevant, anything but a percentage-based system is going to be opaque to someone. Does it matter, for the actual fun in the game to know the absolute chance, or is it sufficient, to get a rough impression of a) how good your character is supposed to be) and b) how difficult a task is?