SOLUTION: A certain game consists of rolling a single fair die and pays off as​ follows: ​$8 for a​ 6, ​$3 for a​ 5, ​$1 for a​ 4, and no payoff otherwise. Find the expected wi

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Question 1158165: A certain game consists of rolling a single fair die and pays off as​ follows: ​$8 for a​ 6, ​$3 for a​ 5, ​$1 for a​ 4, and no payoff otherwise. Find the expected winnings for this game.
Answer by jim_thompson5910(35256)   (Show Source): You can put this solution on YOUR website!

Answer: $2

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Explanation:
Construct a table showing the probabilities of each roll (column 2) and the winnings for each roll (column 1). Column 3 represents the product of columns 1 and 2.
XP(X)W(X)P(X)*W(X)
11/60(1/6)*0 = 0
21/60(1/6)*0 = 0
31/60(1/6)*0 = 0
41/61(1/6)*1 = 1/6
51/63(1/6)*3 = 3/6
61/688*(1/6) = 8/6

X = roll number selected from set {1,2,3,4,5,6}
P(X) = probability of rolling X
W(X) = winnings for rolling X

Add up the results of column 3 to get:
0+0+0+1/6+3/6+8/6 = (1+3+8)/6 = 12/6 = 2

The expected winnings is $2

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