Chapter 2.8, Problem 4DYGI

To determine

To calculate: The expected value and comment that is the game fair. Also tell that does it favor one side or not. A game is played her which is known as carnival game and a person is charged $2 to spin the lucky wheel. If the pointer lands on red then the person wins $3 which results in net gain of $1. If the pointer lands on yellow, then the person gets to spin again the pointer for free which means net gain is $0, If the pointer lands on purple then the person loses $2 that means a loss of $2 and if it lands on blue then the person is paid $6. The lucky wheel is as below:

And the table in which gain of each category is given is as below:

$\begin{array}{cccc}\text{Color}& \text{Gain(}X\text{)}& \text{Probability P(}X\text{)}& \text{Product }X\cdot \text{P(}X\text{)}\\ \text{Red}& \$1& & \\ \text{Yellow}& \$0& & \\ \text{Purple}& -\$2& & \\ \text{Blue}& & & \\ & & \text{Expected Value}=& \end{array}$