A class is conducting an experiment using a six-sided number cube. Each person rolls the number cube 6 times and charts their results. If the results are combined into a class list, which statement would be most correct?

Question

A.
Every student has the same probability of getting each individual number.
B.
Each individual student's data will match the theoretical data.
C.
The experimental probability of the combined data should be closer to the theoretical probability than the individual data.
D.
There is more of a chance a student will get all 6 numbers in their rolls than won't.

Answer 1

The most correct statement regarding the class experiment with the six-sided number cube is:

C. The experimental probability of the combined data should be closer to the theoretical probability than the individual data.

This is because the law of large numbers suggests that as the number of trials (rolls in this case) increases, the experimental probability tends to get closer to the theoretical probability. While individual students may have variation in their results due to the small number of rolls (6), when all the class results are combined, the overall experimental probabilities for getting each number should more closely reflect the theoretical equality (1/6 for each number).

Here’s a quick analysis of the incorrect options:

• A is true but doesn't address the experimental vs. theoretical probabilities.
• B is incorrect as individual students' data may vary due to randomness.
• D is misleading; while it is possible for a student to roll all six numbers, the probability of it happening during just 6 rolls is low.