Question

For the wheel pictured on the right, assume that a person spins the pointer and is awarded the amount indicated by the pointer. Determinethe person's expectation assuming the spinner has not yet been spun.$2What is the expectation?

Answer 1

The expectation value is given by:

$EV=\sum_{i\mathop{=}1}^nx_iP(x_i)$

In this case we just have two options, each with probability 1/2, and the values of x are 2 and 9; then we have:

$\begin{gathered} EV=(2)(\frac{1}{2})+(9)(\frac{1}{2}) \\ EV=2+\frac{9}{2} \\ EV=\frac{13}{2} \\ EV=6.5 \end{gathered}$

Therefore, the expectation is $6.5