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A game is played with the following rules. Two ordinary number cubes, each with six sides labeled 1 to 6, are rolled. After each roll a player is given a certain number of points depending on the outcome.

If the sum is 2 or 12, the player receives +6 points
If the sum is 3 or 11, the player receives +2 points.
If the sum is any other number, the player receives –1 point.

What is the expected value of the number of points a player will receive after a roll?

Question

I will fan and medal!
A game is played with the following rules. Two ordinary number cubes, each with six sides labeled 1 to 6, are rolled. After each roll a player is given a certain number of points depending on the outcome.

    If the sum is 2 or 12, the player receives +6 points
    If the sum is 3 or 11, the player receives +2 points.
    If the sum is any other number, the player receives –1 point.

What is the expected value of the number of points a player will receive after a roll?

anonymous · Answer

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anonymous · Answer

Having 36 possible outcomes;
2 = 6 points 
4 = 2 points 
30 = -1 point 

The expected number of points received is 
(2*6 + 4*2 + 30*-1)/36 
= -10/36 
= -5/18