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  Examples of different modals and how they are used:
Modals Amount of Certainty Examples
Will not/Won't
100% certain I will see you at 7 o'clock.
I will not be at work tomorrow.

May not
Ought to
Ought not to/Oughtn't to
Should not/Shouldn't

50% to 75% certain

Many modals can be used for different amounts of certainty.

The plane should arrive soon.
It shouldn't be hard to write this paragraph. (It should be easy to write this paragraph.)
May not
Might not
Less than 50% certain

I might win the race. (I am hoping to win, but I am not confident.)
I could win a million dollars. (It is possible, but I don't think it will happen.)

Something is possible The weather can be hot in June, but it also can be quite cold in June.
Would not/Wouldn't
Could not/Couldn't
Might not/Mightn't
Something is 100% certain, but there is a condition (if) If I had more time, I would stay and talk longer. (certain) (I do not have more time. I will not stay and talk longer.)

Something is possible only with a condition (if)

*See Conditionals for more information on these modals.

I couldn't do this if you weren't helping me. (possible) (I can do this only because you are helping me.)
Modals Obligation or Freedom to Do Something Examples
Have to
Have got to
Strongly obligated to do something Citizens must obey the laws of the country.
People have to breathe in order to live.

Must not
May not
Can not

Not permitted to do something

Drivers must not drive through red lights. Students may not look in their dictionaries during the vocabulary test.
Had better/Had better not
Should/Should not
Ought to/Ought not to
Might/Might not
Recommending or suggesting that something be done

The student had better do his homework. (The student will get into trouble if he doesn't do his homework.)

The student should do his homework. (It is good for the student to do his homework.)

Will Willing to do something, offering to do something

I'll carry your bag.
I'll pay for lunch.

"Who will offer to paint the door?" "I will!"

Can/Can not
May/May not

Asking or giving permission to do something

Can I have ten dollars?
Might I go home now?
You may not leave now.
Need not/Needn't No obligation to do something You needn't pay the bill. The company has already paid for everything. (This means that it is not necessary to pay the bill.)
Be able to
Ability to do something Mary can play the piano.
Mary is able to play the piano.