I am trying to formulate guidelines for learners of English as a foreign language with regards the use of may/might/could to express possibility. It seems to me that you can use these three modals (almost) interchangeably when expressing possibility.
For example, 'Where's Mary?' 'I'm not sure. She may/might/could be in her room.' or 'It may/might/could rain later on.'.
Are there any differences in use between these three modals? If so, what are they?
It has been suggested that might and could are more tentative than may, but I've seen the opposite suggested too. I'm wary of putting this forward as a rule because I think that in most cases intonation plays a more important role than the modal used.
I'd be really grateful if anyone had some ideas on how I could differentiate between the three.
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Mary Ansell's on-line text, English Grammar: Explanations and Exercises, explains some of the differences among these auxiliaries:

3. Can and Could

The modal auxiliary can is most often used in the Simple conjugation.

The most important meaning of can and could is to be able to.
e.g. He can walk thirty miles a day.
When she was young, she could swim across the lake.
The first example has the meaning, He is able to walk thirty miles a day. The second example has the meaning, When she was young, she was able to swim across the lake.

Like the auxiliary would, could can be used in polite requests and suggestions.
e.g. Could you please tell me how to get to Almond Street?
You could try asking the bus driver to help you.

As indicated in the previous chapter, could can be used in sentences expressing wishes.
e.g. He wished he could visit France.
I wish I could have helped you.

See Exercise 6.

It has also been pointed out that could can be used in either the main clause or the subordinate clause of a statement expressing a false or improbable condition.
e.g. If he were stronger, he could help us push the car out of the snow.
She could have caught the bus if she had left right away.
I would be glad if I could help you.
If he could have solved the problem, he would have felt happier.

See Exercises 7 and 8.

In informal English, can is often used with the meaning to be allowed to.
e.g. He says I can take the day off.
Can I have some more soup?

However, in formal English, it is considered more correct to use the auxiliary may in such situations.
He says I may take the day off.
May I have some more soup?

4. May, Might and Must

One of the meanings of may and might is to be allowed to.
e.g. The members of the organization agree that I may join it.
The members of the organization agreed that I might join it.

The auxiliary must is a stronger form of may and might. One of the meanings of must is to be obliged to or to have to.
e.g. You must provide proper identification in order to cash a check.
They must work harder if they are to succeed.

It should be noted that the meaning of must not is to be obliged not to.
e.g. You must not leave.
He must not speak.
The first example has the meaning, You must stay. The second example has the meaning, He must be silent.

In order to express the idea of not being obliged to do something, an expression such as not to be obliged to or not to have to is generally used.
e.g. You do not have to leave.
He is not obliged to speak.
The first example has the meaning, You may stay, if you wish. The second example has the meaning, He may be silent, if he wishes.

Like could and would, might can be used in polite requests and suggestions. The auxiliaries could, would and might can be used to express differing degrees of politeness:

Degree of Politeness Auxiliary
somewhat polite could
quite polite would
very polite might

Thus, might expresses the highest degree of politeness.
e.g. Might I observe what you are doing?
Might I offer some advice?

See Exercise 9.

May, might and must are also used to express differing degrees of probability:

Degree of Probability Auxiliary
somewhat probable may, might
highly probable must

For instance, may and might are often used in the Simple conjugation to express the idea that an event is somewhat probable.
e.g. You might be right.
It may snow later this afternoon.

Similarly, must can be used in the Simple conjugation to express the idea that an event is highly probable.
e.g. He must be mistaken.

In the following examples, the Perfect conjugations with may, might and must are used to express differing degrees of probability relating to past events.
Rupert might have taken the money, but it seems unlikely.
It is possible he may have called while we were out.
It must have rained last night, because the streets are wet.

I believe 'may' implies a reference to the possibility or permission for something to happen i.e. I may get wet because I don't have an umbrella (i.e. if I had an umbrella it would not be possible for me to get wet), or as in q: 'May I go to store?' a: 'Yes, you may'. 'Might' on the other hand I believe refers to the potential liklihood of something happening i.e. 'I might get wet, because it might rain today' independent of any permitting or limiting factors it is simply stating that there is a chance that the event will happen/the situation is as descibed; If one said 'I may get wet, because it might rain today' I believe there would be an implication that there was some other permitting factor coming into play that the speaker is implicitly referring to through using the word 'may' rather than 'might' (such as not having an umbrella). Similarly if you were to say 'It may rain today' you would be referring to some greater power which is permitting the possibility of rain today, but could restrict it on other days. 'Could' is more similar to 'may' in that it is referring to an ability, however I think it is is more referring to a subjunctive situation such as 'I could go to the store, if I wanted to' or 'I could be there at 8, but I'll likely get stuck in traffic'; additionally there is also an implication that the situation being described following 'could' is less than likely. All that said, I think in the common vernacular, the three words have become used somewhat interchangeably and I doubt anyone will slight a new english speaker for using one incorrectly, when correctness may in fact be altogether subjective.
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Webster's 1828

MAY, n. [L. Maius.]

1. The fifth month of the year, beginning with January, but the third, beginning with March, as was the ancient practice of the Romans.
2. A young woman.
3. The early part of life.
His May of youth and bloom of lustihood.
MAY, v.i. To gather flowers in May-morning.

MAY, verb aux; pret.might.

1. To be possible. We say, a thing may be, or may not be; an event may happen; a thing may be done, if means are not wanting.
2. To have physical power; to be able.
Make the most of life you may.
3. To have moral power; to have liberty, leave, license or permission; to be permitted; to be allowed. A man may do what the laws permit. He may do what is not against decency, propriety or good manners. We may not violate the laws, or the rules of good breeding. I told the servant he might be absent.
Thou mayest be no longer steward. Luke 16.
4. It is used in prayer and petitions to express desire. O may we never experience the evils we dread. So also in expressions of good will. May you live happily, and be a blessing to your country. It was formerly used for can, and its radical sense is the same.
May be, it may be, are expressions equivalent to perhaps, by chance, peradventure, that is, it is possible to be.

MIGHT, n. pret. of may. Had power or liberty. He might go, or might have gone.

1. It sometimes denotes was possible, implying ignorance of the fact in the speaker. Orders might have been given for the purpose.

1. Strength; force; power; primarily and chiefly, bodily strength or physical power; as, to work or strive with all one's might.
There small be no might in thy hand. Deut.28.
2. Political power or great achievements.
The acts of David--with all his reign and his might.
1 Chron.29. l Kings 15.

3. National strength; physical power or military force.
We have no might against this great company that cometh against us. 2 Chron.20.
4. Valor with bodily strength; military prowess; as men of might. 1 Chron.12.
5. Ability; strength or application of means.
I have prepared with all my might for the house of my God--1 Chron.29.
6. Strength or force of purpose.
Like him was no king that turned to the Lord with all his might. 2 Kings 23.
7. Strength of affection.
Thou shalt love the Lord thy God with all thine heart, and with all thy soul,and with all thy might. Deut.6.
8. Strength of light; splendor; effulgence.
Let them that love him be as the sun when he goeth forth in his might. Judges 5.
Shakespeare applied the word to an oath. "An oath of mickle might." This application is obsolete. We now use strength or force; as the strength or force of an oath or covenant.

With might and main, with the utmost strength or bodily exertion; a tautological phrase, as both words are from the same root, and mean the same thing.

COULD, pron. COOD. [The past tense of can, according to our customary arrangement in grammar; but in reality a distinct word, can having no past tense. Could, we receive through the Celtic dialects.]

1. Had sufficient strength or physical power. A sick man could not lift his hand. Isaac was old and could not see. Alexander could easily conquer the effeminate Asiatics.
2. Had adequate means or instruments. The men could defray their own expenses. The country was exhausted and could not support the war.
3. Had adequate moral power. We heard the story, but could not believe it. Th intemperate man could have restrained his appetite for strong drink. He could have refrained, if we would.
My mind could not be towards this people. Jeremiah 15.
4. Had power or capacity b the laws of its nature. The tree could not grow for want of water.
5. Had competent legal power; had right, or had the requisite qualifications. Formerly, a citizen could not vote for officers of government without the possession of some property. AB could not be elected to the office of senator, for want of estate. BC, not being the blood of the ancestor, could not inherit his estate.
6. Had sufficient capacity. The world could not contain the books. John 21.
7. Was capable or susceptible, by its nature or constitution, as of some change. He found a substance that could not be fused.
8. Had adequate strength or fortitude; as, he could not endure the pain or the reproach.
9. Had motives sufficient to overcome objections. He thought at first he could not comply with the request; but after consideration he determined to comply.
10. Had competent knowledge or skill. He could solve the most difficult problems.
There is a difference with "as well"
All three forms can be followed by "well" - could well, may well and might well; but
only may and might can be followed by "as well" - may as well and might as well. You can't say *"could as well".
Anonymousit is simple :
You use may to express premission!
May all yopur problems be small ones. = wish

May I help you? = permission

He may be at home. = probability or permission
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One such grammatical distinction causing much confusion is the use of the modal auxiliaries ‘may’ and ‘might’. When used in the present tense, the two modals are almost transposable, as the difference between the two is merely a very small degree of certainty. However, it has become common practice to use both words in the past tense as though they have the same meaning. In the past tense, may indicates doubt for whether the verb of the clause was carried out and might denotes that the doer had the opportunity to perform an action, but did not. For example, a statement such as If they hadn’t been so brave, I may not have been rescued, could seem reasonable to some native English speakers, however, the speaker was rescued, and therefore might in place of may would be grammatically correct. Conversely, the use of the auxiliary might in a statement such as If I had worn a prettier dress last night, I might have attracted a nice man, the auxiliary may would have made more grammatical sense, as it is not certain that a prettier dress would have resulted in the attraction of a nice man.
MagrietkI am trying to formulate guidelines for learners of English as a foreign language with regards the use of may/might/could to express possibility. It seems to me that you can use these three modals (almost) interchangeably when expressing possibility.For example, 'Where's Mary?' 'I'm not sure. She may/might/could be in her room.' or 'It may/might/could rain later on.'.Are there any differences in use between these three modals? If so, what are they?
I assume your question is restricted to the "unconstrained modals of logic", and that you are not asking about the use of may for permission or could for ability, for example. There are a few differences, particularly with respect to could, which is, in my opinion, only an "honorary" member of the group.

1. could does not operate under negation in the same way as may and might. Whereas may not and might not express the possibility of the negated proposition, could not expresses impossibility unless some unusual stress pattern is provided by the speaker, maybe even with a slight pause after could.
She may be there. She might be there. She could be there.
She may not be there. She might not be there. *She could not be there.
(in the intended reading) (Actually, even may not is a little suspect, as the 'permission' meaning of may might come through in that example.)

2. could almost requires a following be (in the intended reading).
The puppy is thin; he [might / may / could] be [hungry / lost / a stray].
That music sounds like a symphony; it [might / may / could] be by Mozart.
Susan says that the answer is 67, and she [might / may / could] be right.

Otherwise the unintended 'ability' reading or some other anomalous interpretation is too likely:
The drain is blocked; we [might / may / ?could] have to call a plumber.
Liz looks tired; she [might / may / ?could] want to take a nap.
The current rules are too confusing, so the committee [might / may / ?could] develop new rules.

There seems to be no problem if the verb is meteorological, however, because the 'ability' reading is blocked. The weather is not physically able to do things as an agent:
It [might / may / could] rain this afternoon.
The same reasoning applies with other non-agentive situations:
The cake is too big, but the cookies [might / may / could] fit in this box.

3. Unlike might and may, could does not occur with as well. This was mentioned in another post above. (It's debatable whether this is even a case of the "unconstrained modals of logic", but I'll mention it here anyway.)
This party is really dull; we [might / may / *could] as well leave.

4. In American English, the difference between may and might is one of register. may occurs in official announcements and scientific papers, for example, and might occurs more often in ordinary conversation. (Percentages of probability have nothing to do with it!)
Employees may find this information helpful in choosing a health care plan.
For hydrocarbon molecules of this type, electrophoresis may give better results.
We might take a trip to Disneyland this summer.

could would probably not be used in any of the three examples immediately above (in the intended reading).

5. may is not often used in backshifts, but both might and could are.
I [might / may / could] be ready by 10.
I thought (that) I [might / *may / could] be ready by 10.

Thanks CalifJim! I have to teach this in class tomorrow (might, may, could, etc as future possibilities). The book I'm using presents them as all the same, but I knew that "could" just sounded a bit strange used in that way when the subject is a person. I couldn't put my finger on exactly WHY it was strange, though. Your post helped a lot!

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