Ellos vendrían is a transition
I would use
No, no me gusta la biblioteca.
I am hispanic and know spanish from an early age and this is the only one that makes sense.
P.S. In the question it is asking you if you like the library and 1 says Yes, I likes the library 2. Yes, you like the library 3. No I do not like the library and 4 No, you do not like the library, therefore number 3 is correct.
Sorry if that was a little to much
Explanation:
The question you want me to answer is undefined so I will explain from both sides.
Firstly, "necesitas" is wrong. Necesitas is the "tú" conjuagate form of necesitar. It would be used in cases such as:
<em>¿Tú </em><em>necesitas</em><em> un vaso de agua?</em>
The yo form for necesitar would be necesito. Now that we have the correct verb, lets look at the sentence from two sides.
Depending on your question, the sentence can be written in one of two ways.
<em>1. Yo no necesito un papel en la clase de educación física.</em>
<em>2. Yo necesito un papel en la clase de educación física.</em>
In sentence 2, you don't need anything in between the "yo" and "necesito".
Again, this is subjective as I don't really know the question they are asking you. Though I hope I helped you!