We use 'can' or 'may' to give permission. 'May' is formal and used mainly in writing:
'Any person over 18 years may/can apply to join the club.'
They can also be used when asking permission:
'Can I take your umbrella? ~ Of course you can.'
'May we come in?~ Of course.'
'May' is used also to express possibility (= perhaps):
'She may be in the cafeteria.' (= Perhaps she is in the cafeteria.)
'Can' is also used to express possibility. However it is quite different from the possibility expressed by 'may':
You can ski in on the hills. (There is enough snow.)
= It is possible (circumstances permit.)
"She may be in the cafeteria."
= "She COULD BE be in the cafeteria."
Now both sentences express the same meaning (you can use 'could be' instead of 'may/might be' to mean 'perhaps').