MAY is used when
the speaker thinks that what he is saying is perhaps true:
(It is twenty to seven. Jenny wants to phone Paul. The speaker knows Paul
usually arrives home at about 7) The speaker says: Phone him. He may be home
(perhaps he is home, perhaps not).
MIGHT
is used when the speaker thinks the chances of the proposition being true are slim (according to some grammarians).
(Paul wants to know Jenny's phone number.) The speaker says: Ask Sally, she is not one of her close friends but she
might have it.
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