Floor underneath tub missing?!?
Don't sell yourself and blondes short. I hope there isn't a tub over the hole. If there is, I would also make the tub nonexistent at this point, for safety reasons. Water weighs 62.5 pounds per cubic foot. A full bathtub can weigh over 560 pounds from just the water in it (not including the tub and the occupant). The weight on the floor below can come close to 1000 pounds. This weight requires some very sturdy flooring underneath a tub. Often, builders will sister (run two joists side by side, attached to each other) joists running under a tub just to give additional strength. A hole in the floor does not sound encouraging at all. Since I'm not there with you, I can't see the hole and accurately judge exactly what condition your floor is in. Usually, holes under bathtubs are caused by water damage from a cracked tub, leaking drain, diverter, or supply plumbing. Whatever the source, the cause is almost always water damage. If you are renting, I would bring this to the attention of the landlord IMMEDIATELY. This is a serious safety issue. If he shrugs you off, remind him that if you drop in on your neighbor while bathing, he will face a lawsuit that will make fixing the floor seem like buying a pack of gum. If this is your place, get it fixed--NOW! Talk with a licensed framer about the problem. He is probably the best one for the money to address the issue.
Not your house - not your problem. If the tub is supported by joists, then the main disadvantage of not having a floor is that if there is a water leak under the tub, the water will go straight down to the ceiling below and damage the ceiling. If there is a floor under the tub, water will come out into the room and be noticed, so you may be able to fix the leak before it causes a big problem.
In old houses with bathtubs up on legs (claw foot) the tub was installed after the entire room was floored, ie the floor boards continued under the tub. And very old houses were built before there was indoor plumbing - bathrooms added in a closet or partitioned section of a bedroom with existing floors. But it's normal for built in bathtubs to be placed directly on beams (joists) when a house is built, then the floor added afterwords. I suppose that's cheaper - - - and easier to access plumbing from beneath if major repairs are ever needed. We were surprised when remodeling a 1910 house: big bathrooms with great mosaic tile floors and built-in style bathtubs that were way ahead of their time . . . . . we went to move one and found that the tubs mounted directly on beams - no floor beneath - so to save the floors the tub had to stay in the original location.
Usually there is no finished floor under a tub, HOWEVER the tub should be set upon the sub-floor which is usually plywood. If there is none there it could be a real issue, but if you are just renting it is not your issue. Take a few pictures (and keep them) also report your discovery to the manager or owner, this way you are covered.
A hole under the tub?!? Uh there IS supposed to be a floor.