Question 586452: Three unbiased 6 sided dice would be rolled at the same time. Each die had a W stamped on 3 sides and 3 sides that were plain. It would cost $1.00 to play and a player would receive $0.50 for each W they get.
A. What is the sample space for possible outcomes?
B. What is the expected value (how much would you expect to win or lose on average?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! Three unbiased 6 sided dice would be rolled at the same time. Each die had a W stamped on 3 sides and 3 sides that were plain. It would cost $1.00 to play and a player would receive $0.50 for each W they get.
A. What is the sample space for possible outcomes?
www ; wwb ; wbw ; bww ; bbw ;bwb ; wbb ; bbb
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B. What is the expected value (how much would you expect to win or lose on average?
Random number of "w's": 0 ,1 , 2 , 3
Corresponding probabilities: 1/8 ; 3/8 ;3/8 ; 1/8
Random gain to the player:
-100 for 0 w's) ; -50 for 1 w; 0 for 2 w's ; 50 for 3 w's
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E(x) = (1/8)(-100) + (3/8)*-50 + (3/8)*0 : (1/8)*50
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= -100/8 - 150/8 + 0 + 50/8
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= -200/8
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= -25 cents
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Cheers,
Stan H.
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