There are six sides on a balanced die. Each side is numbered 1 through 6. Jimmy is planning on doing an experiment where he would roll a die 400 times. In theory which of the following should Jimmy expect to get after finishing his experiment?

Question

A.
Jimmy should roll more ones than any other number.

B.
Jimmy should roll more fives and sixes than any other number.

C.
Jimmy should roll approximately the same amount of all numbers on the die.

D.
Jimmy should roll odd numbers less than even numbers.

Answer 1

In theory, when rolling a balanced die, each side has an equal probability of occurring. Since there are six sides (numbered 1 through 6), each number has a probability of \(\frac{1}{6}\) of being rolled.

After rolling the die 400 times, we would expect:

• Each number (1, 2, 3, 4, 5, 6) to appear approximately the same number of times.
• Specifically, for a large number of rolls like 400, we would expect each number to appear around \(\frac{400}{6} \approx 66.67\) times.

Based on this reasoning, the best answer is:

C. Jimmy should roll approximately the same amount of all numbers on the die.