Translation:Why don't you have a mirror in the bathroom?
Perche "in bagno" e no "nel bagno". Don't we need the definite article here?
We don't need it, often with rooms in a house it's not used.. (in cucina, in bagno) But if you are speaking about a specific place or a place specified by an adjective etc. you use the definite article. In this case both translations have to be accepted.
Have a look here: https://www.duolingo.com/comment/4390244
With phrases like this, it's a helpful practice to keep a notebook of idioms and write them down as you encounter them. Also, when someone suggests comments which explain something, to click on the link, then bookmark the page in a "language/italian" bookmark folder.
I also often copy the entire comment (including the author's references) and paste it into a text file, which I save in a languages/italian folder on my computer. Helps to build a personal reference library, so you don't have to go searching for these things on the interent.