Indicating Possibility

The words でしょう and だろう can be used at the end of a sentence to indicate that something is probably true. Another phrase that can be used for a similar purpose is かもしれません. The casual form is かもしれない.

Adding this to the end of a short-form predicate will indicate that something is a possibility. As Genki says, use it when "you are not sure what is really the case but are willing to make a guess." It can be used after positive or negative conjugations, in the past or present tense.

昼ごはんの後にジムさんは帰るかもしれません。
Jim may go home after lunch.

庭で犬があったかもしれない。
There may've been a dog in my garden.

明日は外寒いかもしれない。
It may be cold outside tomorrow.

家でたくさん鳥だったかもしれない。
Maybe it was lots of birds in your house.

カナトは馬が嫌いかもしれません。
Kanato may not like horses.

As demonstrated by the last sentence, there's no need to place だ after nouns or na-adjectives when using them with this phrase. They are fine as-is, conjugated or not.