Question

answer in the simplest way

Isabella is studying the fairness of a six-sided numbered cube with numbers 1,2,3,4,5, and 6.

The numbered cube is rolled 36 times, and the numbers on the top side are recorded in the table below.

1 4 1 3 6 2

3 3 5 6 1 6

2 5 4 6 4 2

5 6 1 5 3 6

3 4 3 6 4 1

1 2 5 2 5 3



Based on this data, what conclusion would you make about the fairness of the numbered cube?
Justify your answer.

Answer 1

Counts: 1:6, 2:5, 3:7, 4:5, 5:6, 6:7 (total 36).
Expected each face = 36/6 = 6. Observed frequencies are very close to 6, so there is no evidence the cube is unfair. (A chi-square test gives χ² ≈ 0.67, much smaller than the 5‑df 5% critical value 11.07, so we fail to reject fairness.)