SOLUTION: If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expected value of this game.

Question 1106458: If a gambler rolls two dice and gets a sum of 10, he wins $10, and if he gets a sum of three, he wins $20. The cost to play the game is $5. What is the expected value of this game.
I know that question have already been answered and I saw it, but I dont see how they came up with the answer. If you can help me understant the answer to this question, I would greatly appreciate it.

Answer by rothauserc(4718) (Show Source): You can put this solution on YOUR website!
Consider the sample space for rolling two 6-sided dice, there are 36 possible outcomes
:
(1,1),(1,2),(1,3),(1,4),(1,5),(1,6)
(2,1),(2,2),(2,3),(2,4),(2,5),(2,6)
(3,1),(3,2),(3,3),(3,4),(3,5),(3,6)
(4,1),(4,2),(4,3),(4,4),(4,5),(4,6)
(5,1),(5,2),(5,3),(5,4),(5,5),(5,6)
(6,1),(6,2),(6,3),(6,4),(6,5),(6,6)
:
There are only two that have a sum of three: (1,2) and (2,1)
There are only three that have a sum of ten: (4,6), (5,5), and (6,4)
:
Therefore the expected winning on a role is
:
(2/36) * 20 + (3/36) * 10 = $1.94
:
The gambler paid $5 which means
:
-$5 +$1.94 = -3.06
:
The gambler can expect to lose $3.06 per play on average
:
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