Page 352 - Practical English Usage 3ed - Michael Swan, Oxford

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The structure can be used to criticise. Might have + past participle is used to talk about the past.
You might ask before you borrow my car.
She might have told me she was going to stay out all night.
For the use of could in similar senses, see 124.7.
may and might (8): may/might and can/could
May/might are often used in similar ways to can/could. The main differences are as follows. For more details of these uses, see 121-124 and 338-340.
permission: can/could more common
Can and could are more common than may and might, which are used mostly in a formal style. Compare:
Can I look at your paper?
ExcLlse me, may I look at your newspaper for a moment?
There is an old belief that may/might are more 'correct' than can/could in this case, but this does not reflect normal usage.
'general' possibility: can/could, not may/might
We normally use can and could to say that things are possible in general: people are able to do them, the situation makes them possible, or there is nothing to stop them (see 122). May and might are not used in this way.
She's lived in France; that's why she can speak French. (NOT ••• that's why she may speak French.)
These roses can grow anywhere. (NOT These ffl~ may gHJftJ a"Yft'ltere.) Can gases freeze? (N OT Mily gttSt!3 free2:e?)
In those days, everybody could find a job. (NOT ••• elleryb(j(ly mightji,rd a
j6b:)
chances: may/might/could, not can
To talk about the chance (possibility) that something will happen, or is happening, we use may, might or could, but not can.
Where's Sarah? -She may be with Joe. (NOT She Cd" be ...)
We maygo to the Alps next summer. (NOT Vie am g6 ••• "ext sftmmer.) Might and could suggest a less strong possibility.
It might/could rain this evening, but I think it probably won't. May is not used in direct questions with this meaning.
Do you think you'll go to the ALps? (NOT MilY 16ft gtJ •• •n negative sentences: may/might not and can/could not
May/might not means 'perhaps ... not .. .'
Can/could not can mean 'it is certain that ... not .. .' (see 359.2). Compare:
- It may/might not rain tomorrow. (= Perhaps it will not rain.)
It can't/couldn't possibly rain tomorrow. (= It will certainly not rain.)
- It may not be true. (= Perhaps it is not true.)
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may and might (8): may/might and can/could 345
It can't be true. (= It is certainly not true.)
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