a) Suppose we have a bag with 10 slips of paper in it. Eight slips have 3 on them and the other two have 8 on them. How many 8's do we have to add to make the expected value equal to 6?
b) Suppose we have a bag with 10 slips of paper in it. Eight slips have 3 on them and the other two have 8 on them. How many 8's do we have to add before the expected value is at least 7?
a) If there are 10 slips of paper in the bag, and 8 of them have 3 on them, then the expected value is 3. If we add one 8 to the bag, then the expected value becomes (8 * 1/11) + (3 * 10/11) = 3.63636..., which is still greater than 6. If we add two 8's to the bag, then the expected value becomes (8 * 2/12) + (3 * 10/12) = 5, which is equal to 6. Therefore, we need to add 2 8's to the bag to make the expected value equal to 6. The answer is 2.
