Expressing Certainty and Uncertainty (Present and Past)

CERTAINTY AND UNCERTAINTY (POSSIBILITY) 
PRESENT TIME
 May/Might: There is little difference between them, although MIGHT seems less possible  
                       She might come tonight (Maybe she will come)
Questions: only MIGHT (formal)
Negatives: they must be written in full: He may /might not be at home
Could: 
He could still be at home
Could he still be at home?
He couldn’t be at home.     
Must and Can’t: They are opposites 
He must be at home. (He’s certain to be at home. It also implies a deduction)
He can’t be at home. (I don’t think he is at home. I’m sure he’s not at  home)
PAST TIME
May have and Might have: these both refer to events in the past which are uncertain:
You may have left it on the bus
He might not have gone there ( It  suggests a slight possibility)
Questions are not possible.
Could have: 
It could have been him I suppose.
Could it have been him?
Must have and Can’t have: These also express certainty, but as a deduction (an opinion of what it probably happened)
The butler must have done it (I think that’s what happened) 
You can’t have seen him yesterday, he’s in Australia  (this is my proof that it is impossible)

Exercise. Rewrite the sentences using a modal verb.
1.- Maybe Janet invited him here tonight. Janet...
2.- I’m sure she is quite angry. She...
3.- Perhaps he visited us, but we were away. He...
4.-He hasn’t contacted me. He clearly thought I was unsuitable for the job.  He...
5.- I'm sure she doesn't like onions. She...  

 Solutions 

1. Janet might have invited him here tonight.
2. She must be quite angry.
3. He may have visited us, but we were away. 
4. He must have thought I was unsuitable for the job.
5. She can't like onions.