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.

Step-by-step explanation:

We have that there are total six students to be selected by the principle.

So, the principle chose to roll two dice numbered 1, 2, 3, 4, 5, 6 for the respective students and choose the one whose number is most repeated.

As, the total possible outcomes for rolling of two dice are 36.

So, the probability to choose one student i.e. one number = $\frac{1}{36}$.

Thus, the selection of each student is given by the number $\frac{1}{36}$.

Hence, the principle chose a fair method as each result is an equally likely possible outcome.

Answer 2

Since there are 6 students out of which one needs to be selected, the principal chose two die on which there are six numbers each numbered from 1 , 2, 3, 4, 5, 6.

Since there are two dice, the total possible outcome is 36.

Hence, the probability of getting one number each is 1/36

Hence, the principal used a fair method because each result is an equally likely possible outcome.

Option B is correct.