### Home > GC > Chapter 11 > Lesson 11.2.1 > Problem11-77

11-77.

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 $8$.

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.

$P\left(6\right) · \left(6\right) + P\left(−8\right) · \left(−8\right) + P\left(0\right) · \left(0\right) + P\left(A\right) · \left(8\right) = \text{expected value}$

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

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

$1$

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

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

$−8$