For this case what we should do is fill in the blank with the correct word.
We observe that we are talking about a room.
Therefore, the only private space that can be is a bathroom.
Completing the sentence in Spanish we have:
La habitación tiene un cuarto de baño privado.
The translation of the sentence in English is:
The room has a private bathroom.
Answer:
"baño"
La habitación tiene un cuarto de baño privado.