Question

Suppose you play a game with a spinner. You play each game by spinning the spinner once. P(red) = $\frac{2}{5}$, P(blue) = $\frac{2}{5}$, and P(green) = $\frac{1}{5}$. If you land on red, you pay $\backslash (10$. If you land on blue, you don't pay or win anything. If you land on green, you win $\backslash )10$. Complete the following expected value table.

Short answer

The expected value of the table is shown as below:

Step-by-step solution

Content Introduction

We are given here,

X is equal to winning amount in $

Content Explanation

The expected value table is:

The expected value $\mu$

$$\begin{gathered} SumofX\left(P\right)X=sumofallvaluesinthelastcolumnofabovetable \\ =-4+0+2 \\ =-2 \end{gathered}$$

Therefore, there is a loss of$\$2$on an average every time the game is played.