May John go home?

No, it sounds like you're asking permission for him to go home.

Could it be that John is going home?

Or your choice: Is is possible that John is going home?

1. Can it be that John is going home?

2. Could it be that John is going home?

3. May it be that John is going home?

4. Might it be that John is going home?

Which of the above sentences do you think is incorrect?

Can we say "May John go home?" to mean "Is it possible that he will go home"?

No. That's not the usual interpretation. You could say "Might John go home?" That would be a little more likely to be heard with the meaning "Is it possible that he will go home?" Nevertheless, even with this expression, other interpretations related to permission are also very l

Which of the above sentences do you think is incorrect?

None is strictly speaking incorrect, but 3 is awkward, in my opinion.

CJ

Hi guys,

We do say 'John may go home', to suggest that it is a possibility.

The question form just seems to me to be unidiomatic, probably because of the ambiguity regarding a request for permission.

Best wishes, Clive