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Question

Suppose that you roll a pair of honest dice. If you roll a total of 7, you win $18; if you roll a total of 11, you win $54; if you roll any other total, you lose $9. Fine the expected payoff for this game. 

 

Answer: $-1.00

 

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Answer 1

Possible combinations for rolling a 7: [1,6][6,1][2,5][5,2][3,4][4,3]

P(7)= (1/6)*(1/6)+(1/6)*(1/6)+(1/6)*(1/6)+(1/6)*(1/6)+(1/6)*(1/6)+(1/6)*(1/6)=6/36=1/6

 

Possible combinations for rolling a 11:[5.6][6,5]

P(11)= (1/6)*(1/6)+(1/6)*(1/6)= 2/36=1/18

 

P(2,3,4,5,6,8,9,10,12)= 1- (6/36)- (2/36)=28/36=7/9

 

Expected payout= p(7)*18 + p(11)*54 + p(2,3,4,5,6,8,9,10,12)*(-1) =18*(1/6)+ 54*(1/18)-9*(7/9) = -1