Today I've found out that may well means probably. I know that may is also used to express probability. What is the difference between using "may well" and "may" then?
Some of the examples I've run into are:
You may well be right.
He may well have missed his bus.
I'm wondering if the meaning of these sentences is the same as the meaning of
You may be right.
He may have missed his bus.
Yes, the basic meaning is the same.
Well is simply an adverb modifying may. It means that the event is not merely possible, which is all that the bare may implies, but quite probable.
Note that this must be distinguished from sentences which employ may well in a sense which has nothing to do with probability:
You may well say that.
Here the meaning of may is permissive, and well has its ordinary meaning as the adverbial form of good. The sentence means:
I acknowledge that what you say is quite true. ... or, more simply:
Well said!
