If a player rolls two dice and gets a sum of 2 or 12, he wins $20. If the person gets a sum of 7, he wins $5. The cost to play the game is $3.

Question

1. Construct a probability model for this game in which X is the winning dollar amount in one game and P(X) is the probability of each of these winning amounts. 

 

1. What are the expected winnings in a game?  

 

 

1. Is it “fair” that this game costs $3 to play? Explain. 

 

Answer 1

Prob(2) = 1/36 <--- 1 and 1 a.k.a snake-eyes

Prob(12) = 1/36 <-- 6 and 6 a.k.a box-cars

So Prob(2 or 12) = 2/36 = 1/18

Prob(7) = 6/36 = 1/6 = 3/18 <--- 1+6, 2+5, 3+4, 4+3, 5+2, 6+1

Prob(Loss) = 1 - 1/18 - 3/18 = 14/18 = 7/9

Expected Value = SUM [ Prob(x) * $X ]

(1/18) * 20 + (1/6) * 5 - 7/9*-3

=20/18 + 5/6 - 21/9

= 10/9 + 5/6 - 21/9

= 5/6 - 11/9

= 15/18 - 22/18

= -7/18

= -0.38

you will lose almost 39 cents