SOLUTION: In the carnival game "chuck-a-luck," you pick a number from 1 to 6 and roll 3 dice in succession. If your number comes up all 3 times, you win $3; if your number comes up twice, yo

Question 119633This question is from textbook
: In the carnival game "chuck-a-luck," you pick a number from 1 to 6 and roll 3 dice in succession. If your number comes up all 3 times, you win $3; if your number comes up twice, you win $2; if it comes up once, you win $1; otherwise you lose $1. What is your expected gain or loss? This question is from textbook

Answer by stanbon(75887) (Show Source): You can put this solution on YOUR website!
In the carnival game "chuck-a-luck," you pick a number from 1 to 6 and roll 3 dice in succession. If your number comes up all 3 times, you win $3; if your number comes up twice, you win $2; if it comes up once, you win $1; otherwise you lose $1. What is your expected gain or loss?
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The random variable is "gain" with values 3,2,1,-1
The corresponding Probabilities are:
P(3) = (1/6)^3
P(2) = 3*(1/6)^3
P(1) = 3*(1/6)^3
P(-1) = 1 - 7(1/3)^3
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Expected gain is: 3*(1/6)^3+2*3(1/6)^3+1*3(1/6)^3-1*(1-7(1/3)^3)
Expected gain is (1/3)^3[3+6+3-(0.7407)]= (1/3)^3[11.2593] = 0.4170
Rounding to the nearest cent, expected gain is 42 cents
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Cheers,
Stan H.

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