A class of 30 students 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 is false?

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

1 answer

To evaluate which statement is false, let's analyze each option in the context of rolling a six-sided number cube (or die):

A. There is more of a chance a student won't get all 6 numbers in their rolls than will.

  • This statement is true. With 6 rolls of a die and only 6 faces, it's indeed more likely that not all numbers will appear due to the finite number of rolls.

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

  • This statement is true. When combining the results of many rolls from multiple students, the averages should stabilize and get closer to the theoretical probability due to the law of large numbers.

C. Every student has the same probability of getting each individual number.

  • This statement is true as each roll of the die is independent, and the probability of rolling any individual number (1 through 6) remains 1/6 for every student.

D. Each individual student's data will match the theoretical data.

  • This statement is false. Individual students' data will vary (due to randomness) and will not consistently match the theoretical probabilities, especially with only 6 rolls.

Therefore, the false statement is:

D. Each individual student's data will match the theoretical data.