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 fair six-sided die, each number (1 through 6) has an equal probability of being rolled. Since Jimmy plans to roll the die 400 times, we can calculate the expected outcomes for each number.
The theoretical expectation for each side of the die (1, 2, 3, 4, 5, and 6) is:
- For each number: \( \frac{400 \text{ rolls}}{6 \text{ sides}} \approx 66.67 \)
This means Jimmy should expect to roll each number approximately 66-67 times if the rolls are independent and random.
Given these considerations, the correct answer is:
**C. Jimmy should roll approximately the same amount of all numbers on the die.**
The other options are incorrect because:
- A suggests that ones would be rolled more than any other number, which is not expected in a balanced die.
- B implies that fives and sixes would be rolled more often, which isn’t true either.
- D states that odd numbers would be rolled less than even numbers, which does not hold true for a fair die.
The theoretical expectation for each side of the die (1, 2, 3, 4, 5, and 6) is:
- For each number: \( \frac{400 \text{ rolls}}{6 \text{ sides}} \approx 66.67 \)
This means Jimmy should expect to roll each number approximately 66-67 times if the rolls are independent and random.
Given these considerations, the correct answer is:
**C. Jimmy should roll approximately the same amount of all numbers on the die.**
The other options are incorrect because:
- A suggests that ones would be rolled more than any other number, which is not expected in a balanced die.
- B implies that fives and sixes would be rolled more often, which isn’t true either.
- D states that odd numbers would be rolled less than even numbers, which does not hold true for a fair die.