We can use modal verbs to talk about probability or improbability of something, as well as to make deductions about some facts or events.

 

To talk about something with uncertainty, use modal verbs ‘might’ and ‘could’:

 

Sarah isn’t feeling well. She might have a cold.

 

I have a high temperature. It could be a flu.

 

To describe negative things you are not certain about, use ‘might not’:

 

Your leg is not swollen, so it might not be serious.

 

I can’t reach Tom by phone, he might not be in the city.

 

To speak with more certainty about things in present, use ‘must’:

 

John must be very tired, he’s been staying in bed all day long.

 

They must be absent, I cannot find them anywhere.

 

To speak about something you consider absolutely impossible, use ‘cannot (can’t)’:

 

Jack cannot be at school, I saw him playing basketball at the playground.

 

Pete’s leg can’t be broken, he walked to the doctor without any help.

 

To speak about something that you think definitely happened in the past, use  ‘must have’ with the past participle (for regular verbs, this is the “-ed” form of the verb):

 

I can’t find my socks. My wife must have taken them to the laundry room.

 

Nobody opens the door, my friend must have left the house already.

 

In case you are not sure whether something happened in the past, use ‘may have’, ‘might have’ or ‘could have’ instead of ‘must have’:

 

Cindy didn’t return my call yesterday. She might have forgotten to call me back.

 

I didn’t see who knocked on the door, but it may have been the postman.

 

And finally, if you are absolutely sure that something did not happen in the past, use ‘couldn’t have’:

 

I saw a flash in the sky, but it couldn’t have been aliens, they don’t exist.

 

Paula couldn’t have been at the party last night, she was at work.