throwing a plugged in radio into a tub wouldn't even hurt you cause bath water's much more conductive than a human meatbag, the current would flow to earth thru the path of least resistance which is thru the water surrounding you
this is the same reason linemen's suits/gloves have tiny metal strands woven thru them... it's so they can touch live electrical lines without worrying about getting shocked, the path of least resistance there is their clothes
fishing a plugged in radio out of a tub will likely kill you tho, since your body ends up becoming the only remaining path to ground