Risk probability assesment

Your exam could be marked with a range of possible grades, simplified as on the following state diagram:

To begin with the chances are that you will pass with a standard result. Each 45 minutes (the time allocated for each answer) your grade could go up or down to a neighbouring grade or stay put.

There is a chance that your Genius is so great that the examiner cannot appreciate what you are saying and incorrectly marks it as nonsense.

What is your grade most likely to be after the 3 hour exam?
What (if any) are the steady state results for a group of 14 students?

How can I start this one?