Question 1103446
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The expected value is found by adding all the products of the probability of each outcome and the value of each outcome.<br>
1/36 probability of getting a 2; 2*1/36 = 2/36
2/36 probability of getting a 3; 3*2/36 = 6/36
3/36 probability of getting a 4; 4*3/36 = 12/36
4/36 probability of getting a 5; 5*4/36 = 20/36
5/36 probability of getting a 6; 6*5/36 = 30/36
6/36 probability of getting a 7; 7*-30/36 = -210/36
5/36 probability of getting a 8; 8*5/36 = 40/36
4/36 probability of getting a 9; 9*4/36 = 36/36
3/36 probability of getting a 10; 10*3/36 = 30/36
2/36 probability of getting a 11; 11*2/36 = 22/36
1/36 probability of getting a 12; 12*1/36 = 12/36<br>
The expected value is the sum of all those fractions, which is exactly 0.<br>
So the game is fair at the current price.