Question

Consider the following game. There is a bottle with 20 colored chips inside. There are 2 blue chips, 4 purple chips, 7 green chips, and 7 red chips. You pay $2 and pick one out at random. If you pick a blue chip, you get a prize of $10. If you pick a purple chip, you get a prize of $5. You get nothing for red or green chips. What is the expected value of playing the game?

$2

$0

–$2

–$0.50

Answer 1

Given that, There is a bottle with 20 colored chips inside. There are 2 blue chips, 4 purple chips, 7 green chips, and 7 red chips. You pay $2 and pick one out at random. If you pick a blue chip, you get a prize of $10. If you pick a purple chip, you get a prize of $5. You get nothing for red or green chips.

P(blue chip) = 2/20 = 0.1

P(purple chip) = 4/20 = 0.2

P(green chip) = 7/20 = 0.35

P(red chip) = 7/20 = 0.35

Let X be a prize.

Follwing table shows the probability distribution of X ,

Chip Color	Prize in $ (X)	P(X)
Blue	10 - 2 = 8	0.1
Purple	5 - 2 = 3	0.2
Green	0 - 2 = -2	0.35
Red	0 - 2 = -2	0.35

Expected value of X is,

E(X) = 0

Hence, the expected value of playing the game is $ 0