It isn't very ____________ that Paula is at home, is it?

The word "likely" is the correct choice in this context because it is an adjective used to indicate that something is probable or has a high chance of occurring. The sentence implies that there is some doubt or uncertainty about Paula being at home, which aligns perfectly with the meaning of "likely."

The other options don't fit the grammatical structure or context of the sentence. For instance, "likelihood" would be a noun and would not work as an adjective needed here. "Like" is typically used as a verb or preposition and does not convey the sense of probability required. "Likeable," which describes something or someone that is pleasant or enjoyable, is also unrelated to the context of discussing likelihood or probability. Thus, "likely" is the only choice that logically completes the sentence.