SOLUTION: A) We roll a pair of dice. If the sum of the dice is 7, you pay $30. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is your expected va
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-> SOLUTION: A) We roll a pair of dice. If the sum of the dice is 7, you pay $30. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is your expected va
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Question 1103446: A) We roll a pair of dice. If the sum of the dice is 7, you pay $30. If the sum is not 7, I pay you the number of dollars indicated by the sum of the dice. What is your expected value?
B)What is the price that you should pay to play the game that would make the game fair?
The expected value is found by adding all the products of the probability of each outcome and the value of each outcome.
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
The expected value is the sum of all those fractions, which is exactly 0.
