I was reading in the bath tub once (is that weird) with a radio perched on the edge of the tub. It was plugged into the wall. When I realized what I was doing I froze. THIS IS HOW PEOPLE DIE!!!!
With GFCI's mandatory for bathrooms and kitchens in new builds, I think it's less of a risk today.
Must have been a fairly long cord? Outlets are not ordinarily placed near bathtubs. Not a good idea in any case. What were you thinking?
The danger is touching the appliance (any appliance attached to the mains) while in the tub, or in contact with any plumbing fixture. It there is a fault, a short circuit to the appliance, current can be conducted through your body.
There should not be any danger if the appliance falls into the tub, unless you are a character on a made-for-television police procedural.
It’s kinda okay to use a cell phone.
You should always use GFI outlets in the bathroom, and kitchen, or anywhere near a faucet, though if the circuit breaker is a GFI breaker they shouldn’t be necessary.