Question
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?
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.
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.
Answers
GPT-4o mini
In a balanced die with six sides numbered 1 through 6, each side has an equal probability of landing face up, which is \( \frac{1}{6} \) for each number.
Since Jimmy plans to roll the die 400 times, we can expect the results to distribute evenly among the six possible outcomes. Therefore, after 400 rolls, the expected number of times each number appears can be calculated as follows:
\[
\text{Expected count for each number} = \frac{400}{6} \approx 66.67
\]
This means that, in theory, Jimmy should expect to roll approximately the same amount of all numbers on the die.
Thus, the correct answer is:
**C. Jimmy should roll approximately the same amount of all numbers on the die.**
Since Jimmy plans to roll the die 400 times, we can expect the results to distribute evenly among the six possible outcomes. Therefore, after 400 rolls, the expected number of times each number appears can be calculated as follows:
\[
\text{Expected count for each number} = \frac{400}{6} \approx 66.67
\]
This means that, in theory, Jimmy should expect to roll approximately the same amount of all numbers on the die.
Thus, the correct answer is:
**C. Jimmy should roll approximately the same amount of all numbers on the die.**