Fill in the blanks with the correct modal
Jimmy______have seen me because he walked past without greeting me.

couldn't

The correct modal to fill in the blank is couldn't. The modal couldn't is used to express past inability, and it is the most appropriate modal to use in this context because it conveys the idea that it is unlikely that Jimmy saw you because he walked past without greeting you. If he saw you, he would have greeted you.

The other options are incorrect. The modal might is used to express possibility, but it does not convey the same sense of doubt as couldn't. The modal ought to is used to express advice or a suggestion, but it is not used to express past inability. The modal could is used to express ability, but it does not convey the same sense of doubt as couldn't.