May and Might are modal verbs that are used to show
possibility.  They act like the word "maybe".  This means the
speaker is not sure of the outcome.  

Example:

Tom:        Will you go to the party tonight?
Kathy:      Maybe.

OR

Tom:        Will you go to the party tonight?
Kathy:      I
might go to the party tonight.  


May and Might are used in conditional sentences, especially
the
2nd Conditional and the 3rd Conditional.

Example:        
  • If I won the lottery, I might travel.  However, I don’t know
    for sure.  I might also buy a house.


The difference between
may and might is that may is more
formal.


Here are some tests that use
may and might:

Modal Verbs for Possibility Test
Modal Verbs for Possibility Test 2
Modal Verbs Test
Modal Verbs Test 2
modals
modal verbs
Modal Verbs Tests

May & Might

Business English