Translation:Why don't you have a mirror in the bathroom?
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.
A context search from English to Italian on the word "toilet" shows that your answer should be accepted, even though my impression is that bagno actually means "bathroom" - a place where you can take a bath, wash up - which also has a toilet in it. But the number of context results where bagno = "toilet" seem to very much contradict my notion:
"Pauline, your toilet is clogged again."
Pauline, il tuo bagno è di nuovo otturato.
It is not a good answer. Although it conveys a similar meaning, it is not a literal translation and is not close enough to the meaning of the Italian sentence. The Italian word "hai" translates as "you have" which should be included in the overall translation of the sentence.