Using the expected value, it is found that you should charge $5.14 to have a fair game.
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- The expected value is the sum of each outcome multiplied by it's probability.
The possible outcomes when rolling two dice are:
(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)
- 36 total outcomes.
- 6 have a sum of 7.
- Thus, [tex]\frac{6}{36}[/tex] probability of earning $12.
- 2 have a sum of 2 or 12.
- Thus, [tex]\frac{2}{36}[/tex] probability of earning $36.
- The other 28 outcomes lose x, thus, [tex]\frac{28}{36}[/tex] probability of losing x.
Fair game means that the expected value is 0, thus:
[tex]\frac{6}{36}(12) + \frac{2}{36}(36) - \frac{28}{36}(x) = 0[/tex]
[tex]\frac{72 + 72 - 28x}{36} = 0[/tex]
[tex]28x = 144[/tex]
[tex]x = \frac{144}{28}[/tex]
[tex]x = 5.14[/tex]
$5.14 should be charged for a fair game.
A similar problem is given at https://brainly.com/question/22931679
