Question 806336: If a player rolls doubles when she uses two dice, she wins $5. If the person rolls a 3 or 12, she wins $15. The cost to play the game is $3. Find the expectation of the game.
2(5)+3+12(15)*3=
Found 2 solutions by stanbon, solver91311:
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If a player rolls doubles when she uses two dice, she wins $5. If the person rolls a 3 or 12, she wins $15. The cost to play the game is $3. Find the expectation of the game.
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Random "winnings":: 5.........15........-3
Probabilities:::::: 6/36......3/36......|..27/36
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E(x) = (6*5 + 3*15 - 27*3)/36 = -6/36 = -16 2/3 cents
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Cheers,
Stan H.
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Answer by solver91311(24713)  (Show Source):
You can put this solution on YOUR website!
Refer to the below table of dice results for 2 six-sided dice:
| Sum |
Ways |
# of Ways |
| 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 |
Note that there are 36 different possible results, 6 of which are doubles, 2 of which are 3, and one of which is 12. However, the 12 result is also doubles. Because you don't specify what happens when a 12 is rolled (score 15 for the 12 which overrides the doubles or score 5 for the doubles which overrides the 12, or score 20 for meeting both criteria), I'm going to go with a literal interpretation of the given rules: The player gets 5 for rolling doubles AND 15 for rolling 12.
So the probability of rolling doubles OTHER than 2 sixes = 12 is  , the probability of rolling 12 is  , the probability of rolling 3 is  , and the probability of rolling anything else, which we must presume represents a loss of the initial $3 wager, is  (28 ways to lose out of 36 outcomes).
And then the expected payout is:
You can do your own arithmetic, but in the long run you lose a quarter every time you play.
John
Egw to Beta kai to Sigma
My calculator said it, I believe it, that settles it
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