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When the modal word "can" is used to express possibility, it is used to express general possibility or theoretical possibility rather than specific possibility（http://www.englishpage.com/modals/can.html）, for example "Prices can be high in London" is fine since this is theoretical possibility and "He can be on the bus" is not right since this is specific possibility.

My question is whether this usage is only applied in assertive sentence. Because I saw a sentence on the website "Can this story be true?" and I think "can" here is used to express specific possibility. So I am wondering "can" could be used to express specific possibility in interrogative sentences. Am i right?

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If I understand your question correctly, then yes, you can often swap "Can" in the beginning of a sentence to "Is it possible" -- "Can this story be true?" => "Is it possible this story could be true?" Or "Can you get me some milk at the store, please?" => "Is it possible for you to get me some milk at the store, please?" (Yes, I know that's also a request form. The synonym still holds, as do synonyms of "Are you willing to," etc.)

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Consider:

They may be on the bus.

and

They might be on the bus.

Both mean:
It is possible that they are on the bus.

(AmE seens to prefer might, but only in statements.)

But we don't have a question version of may (= possibility). The following do not work:

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*May they be on the bus?

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*May this story be true?

And "might" is uncommon in questions.

Might they be on the bus?

is grammatical, but unusual. Instead, we use can and could. Could is more usual, but can can be used. Sometimes the difference is one of dialect. To me

Could they be on the bus?

and

Could this story be true?

are more natural than asking the same thing with can. But I'd probably never ask the questions with might.

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  • "May they be on the bus?" is grammatical in other situations, though -- it is asking permission for something to be on the bus. Or, in a more familiar way, "May we be excused from class to go to the bathroom?" (My mother taught our English class. If you asked, "Can I go to the bathroom?" she'd say, "I don't know. Can you?" And then you'd have to rephrase it before you got permission.)
    – A.Beth
    Commented Feb 1, 2015 at 17:32
  • It's hard but not impossible to conceive May they be on the bus? as permissive without an adverbial. As in: May they be on the bus between 10 and 11? And yes, the prescription against can for permission is well-known (I remember the exact moment my 6th grade teacher chided me for asking permission with can.) I think, except for in If I may, that can can be substituted for may in any sentence of permission. What do you say, @A.Beth?
    – user6951
    Commented Feb 1, 2015 at 18:15
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    If I'm understanding your first statement @δοῦλος, I think "I have two dogs; may they be on the bus?" would be a valid request for permission, even without an adverbial. (It'd be a little more correct to say, "May they get on the bus," though considering dogs sometimes charge ahead...) But yes, in common speech -- despite english teachers complaining -- "can" and "may" are interchanged all the time when asking for permission.
    – A.Beth
    Commented Feb 1, 2015 at 21:26

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