A game is set up as follows: Thirteen balls numerated from 1 to 13 are placed in a bag. The balls are mixed up, and then one ball is chosen at random (and then replaced). The player wins according to the following rules.
If the number 1 is drawn, the player loses $20.
If the numbers 11, 12, or 13 are drawn, the player wins $10.
If any other ball (2 –> 10) is drawn, the player wins $2.
Outcome
X Gain
P(X)
XP(X)
a. Find the Expectation of the game.
b. How much should be charged to play this game in order for it to be fair