e.g. The members of the organization agree that I may join it.
The members of the organization agreed that I might join it.
May and might and must are also used to express differing degrees of probability:
Degree of Probability Auxiliary
somewhat probable may, might
For instance, may and might are often used in the Simple conjugation to express the idea that an event is somewhat probable.
e.g. You might be right.
It may snow later this afternoon.
Might, is used when something is permitted
Mary might be in her room (it is permitted for her to be there)
May, is when you simply dont know
Mary may be in her room...(but you really have no idea as to the conditions)