may, might and could - what's the difference

it is simple :
You use might to express possibility
You use may to express premission!  

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.  

If we put these in percentages May is 70% chance that it will happen

Might is 30% chance.

These two were published in the English newspaper ("The Hindu") - Open page section.

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?

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.

CJ

Glad to be of help.

Another post that might be of interest to you and your students is Post:67841.  There I give a basic outline of the meanings and uses of many of the modals, categorized by function.

CJ