The school principal must randomly choose from the six top students in each grade as the school captain each month. To do this, she assigned each student a number, rolled two six-sided dice three times, and selected the student whose number appeared most often. Which of the following best describes the principal's method? a. It's an unfair method because not every student will have the same chance of being chosen. b. It's a fair method because each roll has an equally likely chance of occurring. c. It's a fair method because there are only a limited number of students. d. It's an unfair method because two or more students could have the same number of appearances.
Mathematics · College · Thu Feb 04 2021
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The principal's method is unfair because not every student will have the same chance of being chosen. This corresponds to option (a). The fairness of a selection method depends on whether every student has an equal probability of being selected. With the use of two six-sided dice, the possible outcomes range from 2 (1+1) to 12 (6+6). Some sums, such as 7, are more likely because there are more combinations of dice rolls that result in that sum (1+6, 2+5, 3+4, 4+3, 5+2, 6+1). Less likely sums, such as 2 (only 1+1) or 12 (only 6+6), will occur less frequently. If a student's number corresponds to a sum that has more possible dice combinations, they will inherently have a greater chance of being selected.