The following remarks are for American English.
may and
might are equivalent when they mean that something is
possible.
It may rain today. / It might rain today.
Both mean
It is possible that it will rain today.
Susan may be late for the meeting. / Susan might be late for the meeting.
Both mean
It is possible that Susan will be late for the meeting.
might is more usual in ordinary conversation.
may is more usual in writing, especially academic writing.
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On the other hand, if you are asking permission, use
can or
may (usually with
I).
may is more formal and refined. Many people consider it more polite. But in most ordinary conversations,
can is used.
Can I take this seat? / May I take this seat?
Can I buy you dinner? / May I buy you dinner?
Can I have your address? / May I have your address.
If you use
might in these patterns, you are being very tentative, even timid. This formula with
might is very rare in most ordinary conversations in the U.S.
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In summary, in AmE you rarely need the word
may, except for formal situations. Use
might for possibility and
can for permission.
CJ