It is used in the same way as may to talk about the present and future. The difference is that might usually refers to situations which are less probable or less definite. Might also replaces may in the past indirect speech.
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CalifJimShe may have taken the bus. = She might have taken the bus. (possible that ... did)So both of them can indicate past time with the present perfect and only with this tense, is that so?
Thinking SpainSo both of them can indicate past time with the present perfect and only with this tense, is that so?Yes. Because may and might are modal verbs, these aren't really 'present perfect' tenses. You might say that they are 'modal perfect' tenses. The have has a different function here than it would have in a true present perf
AnonymousIs this use of the modal verb "might" correct in what I think is a habitual (repeated) action setting that is in the past?No. I don't even understand it. Dancing and praying? I don't see any connection. Sorry.
She danced a little. He might lift her hands and pray.
AnonymousCan we use the modal verb "might" here.Yes, you can use "might" there.
(made-up story) ...