Question

A school principal has to choose randomly among the six best students in each grade to be the school captain every month. For that purpose, she assigned each student a number. Then she rolled two dice numbered from 1 to 6 three times and selected the student whose number was repeated most often.
Which of the following best describes the method used by the principal?

A. It's an unfair method because each student will not post the same outcomes.

b. It's a fair method because each result is an equally likely possible outcome.

c. It's a fair method because it's a limited number of students.

d. It's an unfair method because two or more students could get the same results


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Answer 1

Answer: b. It's a fair method because each result is an equally likely possible outcome.

The number of students is same as the number of the sides of the dice. In this scenario, the school principal will roll two dices three times and the number that repeated most will be chosen. For every dice, all number will have equally likely possibility so the randomization is fair.
But it will have a problem if the 6 dices give 6 different number, so there is a chance to get draw result. It doesn't have any correlation with fairness though.