Tony Vargas
Legend
Sure. If the DM decides whether to set the DC above or below the PC's passive score. He could always roll, before-hand.While this might be true and while passive perception works mechanically (i.e. it saves time due to a bunch of rolls not having to be made at the table), it does an extremely poor job of being fair.
Say, for example, that a given PC has a passive perception of 13.
Any trap that the DM assigns a DC of 13 or less has 100% chance of being found.
Any trap that the DM assigns a DC of 14 or more has a 0% chance of being found.
So whether a given trap can be found or not is determined by the DM, it's not determined by the player/PC getting lucky or unlucky.
Passive perception and similar concepts are great not just because they streamline things, but because they avoid the inane charade of the DM calling for perception rolls only to say 'you don't notice anything,' and have the players go into paranoia mode. Then, eventually, the DM gets the bright idea of calling for rolls for no reason. Gets pretty silly. They're also, mechanically, more 'fair,' or less swingy, anyway, because they avoid contested rolls...