Question

The table shows the number of grade 7 and grade 8 students on the student council at Jeremy’s school.

Number of Students
Grade 7 17
Grade 8 34


Every day, two student council members are randomly chosen to read the morning announcements. Students cannot be chosen more than once to read the announcements. Jeremy designed a simulation for the selection of the students and gathered data to predict the probability that a seventh grade student will be chosen. In Jeremy’s simulation, he rolls two number cubes in each of 40 trials. In each trial, a cube landing on 1 or 2 represents a student in grade 7 being selected, and a cube landing on 3, 4, 5, or 6 represents a student in grade 8.

Which statement best describes the flaw in Jeremy’s model?
A- The number of sides on a cube does not match the number of grade levels.
B- The number of sides on a cube is not a factor of the total number of students.
C- The number of outcomes representing each grade level does not change after the first student is chosen.
D- The number of outcomes representing a student in grade 7 is not the same as the number representing a student in grade 8.

Answer 1

C) The number of outcomes representing each grade level does not change after the first student is chosen.

Explanation:

Answer 2

The answer to this is C. Although the initial ratio of Grade 7 to Grade 8 students is 17:34, which is 1:2, and which can be represented well by the 6 sides of the cube by putting 1 and 2 as Grade 7 and 3-6 as Grade 8, the problem with the cube rolls is that the probabilities will not change after students are chosen. The problem states that students cannot be selected more than once, so the cube roll will only work the first time, and may not be accurate for subsequent rolls.