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What do theses ones mean?

1. We cannot release any information about this suspect but we do know that he may have been to California.

2. We cannot release any information about this suspect but we do know that he might have been to California.

Thanks.
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My two cents.

I know that everybody says that the difference is that the probability expressed by "may" is greater than the probability expressed by "might". Nevertheless, I never detect such a difference. If anything, I sometimes take "may" to connote the more remote probability.

Usually though, the only difference I feel is that of register. It seems to me that "might" is the preferred form for most ordinary people in everyday conversation. "may" is a bit more high class, while meaning exactly the same thing (to me, anyway).

CJ
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Garner, Modern American Usage:
"if it's a purely hypothetical question, might would be preferable"
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Comments  
The probability expressed is slightly less for might than for may.

He may have been to California.

He might have been to California, but I doubt it.
"May" is normally a stronger supposition/possibility that "might".
 CalifJim's reply was promoted to an answer.
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Jack

With regard to your post - where do these sentences come from? Which was actually used? I find it easier to work from real data and presumably only one of these examples is 'real'.

Lewis (in the English Verb) argues that 'might' indicates greater remoteness ( in terms of time, likelihood, relationship) of the event from the speaker. I feel the first sentence, if real, needs to have 'recently' or 'may have been living' in the sentence, giving the remark greater 'closeness'.

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 Marius Hancu's reply was promoted to an answer.