MODAL VERBS in the past:

Past possibilities:

John was sent out of class. 

 - He could have been disturbing his classmates. 
 - He might have not been paying attention. 
 - He may have been distracted. 

Contrast between a past possibility and what really happened:

 She was throwing rocks but nobody got hurt.

 - She could have hurt somebody.
 - She might have got into trouble. 

Being sure about something in the past

He didn't come to school today.

 - He must have fallen ill.
 - He must have missed his bus. 

Being sure about something negative or something impossible in the past

 She failed the exam.


- She can't have studied much. 
- She can't have paid attention during the lessons.