Suppose we have a bag with 10 slips of paper in it. Eight of these have a 3 on them and the other two have a 9 on them.
a) What is the expected value of the number shown when we draw a single slip of paper?
b)What is the expected value of the number shown if we add one additional 9 to the bag?
I think the expected value would be 3 x 1/10 = .3 there are 8 of these = .24
9 x 1/10 = .9 there are 2 of these = 1.8 sum = 4.2
(8x 3 + 2 x 9 ) / 10 = 4.2
now add a '9' piece of paper 3 x 1/11 x 8 = 2.1818
9 x 1/11 x 3 = 2.4545 sum = 4.63
[(8x3)+(3x9)]/11 = 4.63