Emma and Eddie both want to choose their family's dinner entrée. Emma prefers burgers, and Eddie would like to order pizza. To determine who gets to pick, their dad suggests rolling a pair of fair dice. If the sum of the dice is 4 or 10, then Emma will pick dinner. If the sum is 2, 3, 11, or 12, then Eddie will pick dinner. They will roll the dice again if any other number is rolled. Is this a fair way to decide? Explain. (Hint: There are 21 total possibilities when rolling a pair of dice.)

A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
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Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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Emma and Eddie both want to choose their family's dinner entrée. Emma prefers burgers, and Eddie would like to order pizza. To determine who gets to pick, their dad suggests rolling a pair of fair dice. If the sum of the dice is 4 or 10, then Emma will pick dinner. If the sum is 2, 3, 11, or 12, then Eddie will pick dinner. They will roll the dice again if any other number is rolled. Is this a fair way to decide? Explain.
(Hint: There are 21 total possibilities when rolling a pair of dice.)
a
No, it is not fair because there is a higher probability of rolling 2, 3, 11, or 12, so Eddie will most likely choose dinner.
b
Yes, it is fair because both Emma and Eddie have an equal probability of choosing dinner.
c
No, it is not fair because there is a higher probability of rolling 4 or 10, so Emma will most likely choose dinner.
d
No, it is not fair because there is a greater probability that they will roll a number other than 4, 10, 2, 3, 11, or 12.
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