Suppose we have a bag with $10$ slips of paper in it. Eight slips have a $3$ on them and the other two have a $9$ on them. What is the expected value of the number shown if we add two additional $3$'s to the bag?
The expected value is 48/11.
3(10/12) + 9(2/12) = 30/12 + 18/12 = 48/12 = 4
