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Hi teachers,
Can I ask about possibilities as below?

Situation1 :The window was broken yesterday .Now I ask Jim :

Who can / could have broken it ?
Who may have broken it ?
Who might have broken it ?

Situation 2 : I don't know whether Jack will come to Ann's birthday party or not.Now I ask my friend :

May Jack come to Ann's birthday party ?
Might Jack come to Ann's birthday party ?

Can Jack come to Ann's birthday party ?
Could Jack come to Ann's birthday party ?

Situation 3: Jim said he would come here by 8 o'clock but now it is already 8.30 and we don't see him around here.Now I ask my friend:

Can /Could /might /may he have lost his way ?

Thank you in advance
Comments  
Hi Tuongvan, you have continuing problems with spacing around punctuation.

You do not need spaces before question marks:

Who could have broken it ? -- incorrect (or non-standard)

Who could have broken it? -- correct

When you use a full stop, comma, colon or semicolon, put a single space after it, and no space before.

Situation1 :The window was broken yesterday .Now I ask Jim : -- incorrect

Situation 1: The window was broken yesterday. Now I ask Jim: -- correct

As far as your other questions are concerned, I've tried to describe my usage below, as best I can.

1)

Who could/can have broken it? -- Both OK.
Who might have broken it? -- OK, but to me tends to suggest that there are a known group of suspects.
Who may have broken it? -- not natural to me.

2)

Is Jack coming to Ann's birthday party? / Is Jack going to come to Ann's birthday party? -- These are the most common ways to ask.
Will Jack come to Ann's birthday party? -- OK.
Might Jack come to Ann's birthday party? -- Possible; more polite, and tends to imply greater doubt about whether he'll come.
May Jack come to Ann's birthday party? -- Could theoretically mean "does Jack have permission to come", but this use is somewhat old-fashioned, and the sentence is not very natural to me.
Can Jack come to Ann's birthday party? -- Fine. Asks if he is able to come (has permission/opportunity).
Could Jack come to Ann's birthday party? -- Same, but expresses greater doubt/politeness.

3)

Could he have lost his way? -- Fine.
Can he have lost his way? -- OK, but less likely.
Might he have lost his way? -- OK; more formal.
May he have lost his way? -- Not natural to me.
TuongvanSituation1 :The window was broken yesterday .Now I ask Jim :

Who can / could have broken it ?
Who may have broken it ?
Who might have broken it ?
Your best choices here are: Who [could / might] have broken it? Personally, I wouldn't use may or can.
TuongvanSituation 2 : I don't know whether Jack will come to Ann's birthday party or not.Now I ask my friend :

May Jack come to Ann's birthday party ?
Might Jack come to Ann's birthday party ?

Can Jack come to Ann's birthday party ?
Could Jack come to Ann's birthday party ?
You want to know "yes" or "no" about this, so your best choice is: Is Jack coming to Ann's birthday party? A modal verb is not needed here. can and could focus on Jack's ability, and even if Jack is able to come to the party, he might not come anyway, so that's not getting the answer you want. may focuses on whether he has permission to come to the party, and you're not interested in that either. might asks only if it's possible, and we can certainly assume that yes, he might come to the party, and yes, he might not come to the party, so that's not getting you anywhere either. (Every action in the universe either might happen or might not happen -- so to be told that something might happen is usually not to be told very much!)
TuongvanSituation 3: Jim said he would come here by 8 o'clock but now it is already 8.30 and we don't see him around here.Now I ask my friend:

Can /Could /might /may he have lost his way ?
In order, best first, I'd say could, might, can. I wouldn't use may here, though some speakers might. (I know you are interested in the usage of modal verbs, but again, a modal verb is not necessary: Do you think he lost his way? The real meaning, I think, is not even a question, but more like: I wonder if he (has) lost his way.)
____
In general, when speculating on the cause of something or on the identity of some unknown person or thing in the past, a question with could have is the best choice:
Who could have done it? What could have caused it? Could he have lost his way? Could anyone have predicted it? Where could they have put it? Where could I have seen it? How could you have forgotten it? Who could have taken it? Why couldn't they have brought it earlier? What could we have done differently?

CJ
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Thank you Mr Wordy and Califjim ever so much,but I am still confused about these 02 grammar points:

1/My Michigan grammar book says that we cannot use MAY and MIGHT to ask about possibility,but sometimes I still see MIGHT used in questions about possibility:Might he be waiting outside?I womder whether I can say "Might it rain tonight?"or"Might she come here tonight?".

2/My grammar book says we can use another modal to replace WOULD in the oast unreal condition like MIGHT or COULD.I wonder whether I can use MUST or not: " If I had met him yesterday,he must have been very happy"(but I did not mee him.)

Your continued help would be greatly appreciated.

Best wishes
1. Too formal, but you can find examples in the literature:
http://books.google.com/books?q=%22might+it+rain%22&lr=&sa=N&start=10

2. No, use would. Must have been means probability.
1. Regardless of what your grammar book says ought to be the case, native speakers do use "might" at the start of a sentence to ask about possibility (as opposed to permission). This does not seem wrong to me. It is, however, more formal-sounding than other options, and less likely in everyday conversation. "May" in the same role is, to me, strange/incorrect. (Other uses of "might" to ask about possibility are natural and common in everyday conversation as well as in more formal writing; for example, "I wonder if it might rain...", "Do you think it might rain?", etc.)

2. "Must" does not work in this sentence. Assuming you mean that he would have been happy because of the meeting (had it happened), "would" is the word to use.
Students: We have free audio pronunciation exercises.
>"I wonder if it might rain...", "Do you think it might rain?"
I think that these suggestions by Mr. Wordy are more natural than yours.
Tuongvansays that we cannot use MAY and MIGHT to ask about possibility,but sometimes I still see MIGHT used
Perhaps might is not used very much, but, as you have seen, it is used sometimes. It sounds almost too formal, but it is used. On the other hand, may is not used to ask about possibility, just as your book says.
TuongvanI wonder whether I can use MUST
Not usually. Not as part of a Type 2 or Type 3 conditional.
CJ
Thank you ever so much again Mr Wordy, Marius Hancu, and Califjim for your great help .I understand completely now.
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