We use must, can’t, may, and could with an infinitive (e.g. go, work, play, earn):

Look at this example with must:

• Agnieszka has lived in Warsaw all her life. She must be (= From what we know, we can be certain that Agnieszka is Polish.)

We use must to say that we are certain:

• That must be Paul. They said he was tall with bright red hair.
• It’s getting dark. It must be quite late.
• You haven’t eaten all day. You must be hungry.

• Agnieszka has lived in Warsaw all life and has a Polish name. She can’t be French. (= From what we know, we can guess that Agnieszka is not French.)

We use can’t to talk about impossibility:

• They know the way here. They can’t be lost!
• If Smith was at work until six, he can’t be the murderer.

Look at this example with may:

• A: Lena’s not in her office. Where is she?
• B: It’s one o’clock. She may be in the canteen. (= From what we know, perhaps she is in the canteen.)

We use may, might, and could for something that is possible but not certain, now or in the future:

• They might come by car tomorrow. (= Maybe they will come by car tomorrow.)

Now look at this example with may not:

• A: I’ve phoned Abigail a few times, and there’s no answer.
• B: She may not be at home. (or She might not be …) (= Perhaps she is not at home.)

Could not is not possible here.