Examine the spinner at right. Assume that the probability of spinning a $-8$ is equal to that of spinning a $0$.  

1. Find the spinner’s expected value if the value of region $A$ is $8$.

   Hint (a):

   Find the expected value of a single spin by finding the product of the probability and the value for each region. Find the sum for all the regions.

   More Help (a):

   $\left(6\right)\cdot\left(\frac{1}{2}\right)+\left(-8\right)\cdot\left(\frac{1}{8}\right)+\left(0\right)\cdot\left(\frac{1}{8}\right)+\left(8\right)\cdot\left(\frac{1}{4}\right)=\text{expected value}$

2. Find the spinner’s expected value if the value of region $A$ is $-4$.

   Hint (b):

   Use the same equation from part (a), but put a $-4$ in place of the $8$ for the value of $A$.

   Answer (b):

   $1$

3. What does the value of region $A$ need to be so that the expected value of the spinner is $0$?

   Hint (c):

   Use the same equation from part (a), but put a $0$ in place of the $8$ for the value of $A$.

   Answer (c):

   $-8$