For the wheel pictured on the right assume that a person spi

For the wheel pictured on the right, assume that a person spins the pointer and is awarded the amount indicated by the pointer. If it costs $3 to play the game, determine the expectation of a person who plays the game and the far price to play the game. What is the expectation?

Solution

a) Expectation value of the game = P(arrow coming in $9 location) * $9 (price amount) + P(arrow coming in $5 location) * $5 (price amount)

SInce the P(arrow coming in $9 location) = P(arrow coming in $5 location) = 180 degrees/360 degrees = 0.50

Expectation value of the game = 0.5 * $9 + 0.5 * $5

=> 0.5 * ($9 + $5)

=> 7$

b) Fair price of the game should be $7