Modal verbs to express possibility or certainty

We use modal verbs must may could might can't to show how certain we are about something. We use 'must' when we are almost certain about something, 'must' + infinitive without 'to':

That must be Jack. He always rings at this time.

The past of 'must' is 'must have done / been':

He must have finished work by now. He must be on his way home.

'May' is used to say that something is a possibility, the speaker is not expressing an opinion,'may' + infinitive without 'to':

I'm going to fill the bath. Jack may want a bath when he arrives. He sometimes does.

The past of 'may' is 'may have done / been':

Or he may have had a shower before he left work.

'Could' is like 'may':

I suppose he could have spent the day in the office, so he may not want a bath.

'Might' is used to say something is possible but we think it's unlikely:

Of course, he might stop at the pub for a drink on his way home. He sometimes does, but he didn't say so on the phone.

The past of 'might' is 'might have done / been':

He's very late. He might have had an accident, although he's a very careful driver.

Modal verbs to express possibility or certainty

We use 'can't' to say we think something is impossible, we have evidence for thinking this. 'Can't' is the negative of 'must'. 'Can't' + infinitive without 'to':

He can't be at the cinema. He never goes to the cinema without taking me.

The past of 'can't' is 'can't have done / been':

He can't have gone with someone else. He wouldn't dare!