MAY (permission (reported speech (He told me that i might smoke in the…
He told me that i might smoke in the room
+the form might to express a more polite request
Might I join you?
prohibition (not common) is expressed by can/must
you may not smoke here.
Possibility due to the circumstances
indicates that the action wasn't carried out owing to certain circumstances
he might have fallen ill if he hadn't taken the medecine
you may order a taxi by the phone