Question

The following game is played in a casino. The participant would roll two fair dice and...

The following game is played in a casino. The participant would roll two fair dice and if they sum to 8 or higher, the participant wins 4$ otherwise they lose 3$. What is the expected payout the casino will make as each game is played?

Math   Statistics-And-Probability   
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Answer #1
sum of the dice list of outcomes favourable to sum number of outcomes favourable to sum
2 (1,1) 1
3 (1,2),(2,1) 2
4 (1,3),(2,2),(3,1) 3
5 (1,4)(2,3),(3,2),(4,1) 4
6 (1,5),(2,4),(3,3),(4,2),(5,1) 5
7 (1,6),(2,5),(3,4),(4,3),(5,2),(6,1) 6
8 (2,6),(3,5),(4,4),(5,3),(6,2) 5
9 (3,6),(4,5),(5,4),(6,3) 4
10 (4,6),(5,5),(6,4) 3
11 (5,6),(6,5) 2
12 (6,6) 1

number of case in which participant wins $4=5+4+3+2+1=15

number of case in which participant lose $ 3=21

probability distribution table

X 4 -3
P(X) 15/36=5/12 21/36=7/12

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