# 8.5.27Question HelpA pair of fair dice is rolled once. Suppose that you lose \$11 if the dice sum to 4 and win \$14 if the dice sum to 11 or 12. How much should you win or lose if any othernumber turns up in order for the game to be fair?\$To keep the game fair, you shouldif the dice sum to any other number.(Do not round until the final answer. Then round to the nearest cent as needed.)

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12 views help_outlineImage Transcriptionclose8.5.27 Question Help A pair of fair dice is rolled once. Suppose that you lose \$11 if the dice sum to 4 and win \$14 if the dice sum to 11 or 12. How much should you win or lose if any other number turns up in order for the game to be fair? \$ To keep the game fair, you should if the dice sum to any other number. (Do not round until the final answer. Then round to the nearest cent as needed.) fullscreen
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Step 1

The sample space of the 36 possible outcomes for a pair of fair dice is, help_outlineImage Transcriptionclose(11).(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) S = |(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) fullscreen
Step 2

The pairs that give a sum of 4 are (1,3), (2,2) and (3,1).

So, the probability of getting a sum of 4 is,

P(4) = 3/36

And the pairs that give a sum of 11 or 12 are (5,6), (6, 5) and (6,6).

So, the probabili...

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