"may" and "may not"

I've noticed that "may not" is used in English like "can't" or "not allowed". Why?

I always thought that, for example, if "may" means 33% probability ("he may do this" => "occassionally he may do this"), then "may not" would mean 100-33% (like "he usually does, but may happen so that he doesn't do this"), but apparently everyone means by that "can't" ("you may not take your notes to the exam"). Then how do I say with 1 modal verb a sentence like "may be so that he doesn't do this, though he usually does"?

Think of "may not" as "can not/can't".

"You can not do this." effectively means the same as "You may not do this" when in the context of a command.

I am not sure what you mean in the second part of your question but I'll try.

It's possible that he didn't do this.....but he usually does!

or

Maybe he didn't do this....but he usually does.

"He may go to the cinema" can mean two things:

1. He might go to the cinema.
2. He is allowed to go to the cinema.

Traditionally, Can/Can't and May/May not were not interchangeable.

Can / Can't really should only be used to express the physical ability of doing somthing.

Like if a boy asks his teacher "Can I open the window", in proper English he is not asking if he is allowed to, he is asking if he phyiscally has the ability to open the window, or if the window will open if he tries to open it.

If he wants to ask for permission to open the window he should say "May I open the window".

Quote:

---

Originally Posted by detail

Then how do I say with 1 modal verb a sentence like "may be so that he doesn't do this, though he usually does"?

---

'He may not do this' :)

Like TATY said, this can mean two things:

1) He might not do this

2) He is not allowed to do this

In Brittish English, "May (I)" = Am (I) allowed, and "Can" indicates an ability to do something;
In American English, very frequently, "Can" is used in both cases

Thanks, now it's clear. @DDT: I meant that I wanted to express the sense of that sentence in one auxiliary verb. So, it's "he might not do this". Thanks for help!

found my own misprint:

Quote:

---

"you may not take your notes to the exam"

---

There was a discussion a while back about this very subject. I'm too lazy to look for it but maybe you can find it.