Modals of Possibility

Several modal verbs show possibility. They are Might, May, Could, and Must. All of these are different ways to say maybe.

STRUCTURE

Modal Verb + Base Verb
May/Might/Could/Must + Base Verb

Examples:
I may eat dinner at 7:00pm.
She might work late tonight.
They must be tired.

May
May shows possibility in the present or the future.

Present: Where are my keys? They may be in the car.
Future: I may go to the party tonight.

May is formal and is often found in writing.
Side effects of this medication may include upset stomach and fever.

Might
Possibility in the present or future.

Where are my keys? They might be in the car.
I might go to the party tonight.

Might is less formal than may, and is more common in conversation

Could
Something is possible in the present or future.

Present: Where are my keys? They could be in the car.
Future: We could go to the party tonight.

Could shows options, or possibility.

Must
Certainty, or the belief of certainty, from the speaker.

Certain:
Everyone is wearing a jacket. It must be cold.

Belief of certainty:
He was running for 2 hours. He must be tired.
(Although it seems obvious, it is not a fact that the runner is tired.)

Have to
Certainty, or the belief of certainty, from the speaker.

Certain:
Everyone is wearing a jacket. It has to be cold.

Belief of certainty:
He was running for 2 hours. He has to be tired.
(Although it seems obvious, it is not a fact that the runner is tired.)

Have to is much less formal than must, and is common in conversation.

Past Possibility
May, Might, and Could are all used to show possibility in the past.

Modal Verb + Have + Past Participle

He might have brought the cake.
She may have gone home early.
They could have worked late.

Must can be used in the same way to show certainty in the past.
He must have won the game.

Might Not vs. Could Not
Although Might and Could express possibility in a similar way, the negative forms of Might and Could are different.

Might not shows that something probably is not true.
These books might not be the teachers.

Might not shows that something probably will not happen in the future.
I might not go to the party tonight.

Could not shows that something is impossible.
This could not be the only book available.
She could not know who my friend is. They have never met.

taken from:

http://www.learnenglish-online.com/grammar/modals/possibility.html