Mary rolled a number cube 100 times and got the following results. Outcome Rolled 1 2 3 4 5 6 Number of Rolls 14 15 21 20 18 12 Fill in the table below. Round your answers to the nearest thousandth. (a) From Mary's results, compute the experimental probability of rolling a 1. 10 (b) Assuming that the cube is fair, compute the theoretical probability of rolling a 1. 7 (c) Assuming that the cube is fair, choose the statement below that is true: As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. As the number of rolls increases, we expect the experimental and theoretical probabilities to become farther apart. The experimental and theoretical probabilities must always be equal.
Mary rolled a number cube 100 times and got the following results. Outcome Rolled 1 2 3 4 5 6 Number of Rolls 14 15 21 20 18 12 Fill in the table below. Round your answers to the nearest thousandth. (a) From Mary's results, compute the experimental probability of rolling a 1. 10 (b) Assuming that the cube is fair, compute the theoretical probability of rolling a 1. 7 (c) Assuming that the cube is fair, choose the statement below that is true: As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal. As the number of rolls increases, we expect the experimental and theoretical probabilities to become farther apart. The experimental and theoretical probabilities must always be equal.
Algebra & Trigonometry with Analytic Geometry
13th Edition
ISBN:9781133382119
Author:Swokowski
Publisher:Swokowski
Chapter10: Sequences, Series, And Probability
Section: Chapter Questions
Problem 77RE
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![## Probability and Statistics: Experimental vs Theoretical Probability
### Problem Statement
Mary rolled a number cube 100 times and obtained the following results:
| Outcome Rolled | 1 | 2 | 3 | 4 | 5 | 6 |
|----------------|----|----|----|----|----|----|
| Number of Rolls| 14 | 15 | 21 | 20 | 18 | 12 |
### Exercises
Fill in the table below. Round your answers to the nearest thousandth.
1. **(a) From Mary's results, compute the experimental probability of rolling a 1.**
\[
\text{Experimental Probability} = \frac{\text{Number of Rolls of 1}}{\text{Total Rolls}}
\]
\[
\text{Experimental Probability} = \frac{14}{100} = 0.14
\]
2. **(b) Assuming that the cube is fair, compute the theoretical probability of rolling a 1.**
\[
\text{Theoretical Probability} = \frac{1}{6} \approx 0.167
\]
3. **(c) Assuming that the cube is fair, choose the statement below that is true:**
- \( \boxed{} \) As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
- \( \boxed{} \) As the number of rolls increases, we expect the experimental and theoretical probabilities to become farther apart.
- \( \boxed{} \) The experimental and theoretical probabilities must always be equal.
### Explanation
In the given problem, Mary rolled a cube and recorded the number of times each outcome occurred. The table above summarizes her results.
To find the **experimental probability** of rolling a 1, we divide the number of times 1 was rolled by the total number of rolls:
\[
\frac{14}{100} = 0.14
\]
The **theoretical probability** assumes that the cube is fair. Therefore, the probability of rolling any single number (e.g., a 1) is:
\[
\frac{1}{6} \approx 0.167
\]
We also consider the nature of probability. If a cube is fair, as the number of rolls increases, the experimental probability](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F6d7590ab-1e8b-4f01-9940-34be16d61a30%2F6c327b40-ed2f-435e-9817-96b59218ca52%2Fb9xbuk_processed.jpeg&w=3840&q=75)
Transcribed Image Text:## Probability and Statistics: Experimental vs Theoretical Probability
### Problem Statement
Mary rolled a number cube 100 times and obtained the following results:
| Outcome Rolled | 1 | 2 | 3 | 4 | 5 | 6 |
|----------------|----|----|----|----|----|----|
| Number of Rolls| 14 | 15 | 21 | 20 | 18 | 12 |
### Exercises
Fill in the table below. Round your answers to the nearest thousandth.
1. **(a) From Mary's results, compute the experimental probability of rolling a 1.**
\[
\text{Experimental Probability} = \frac{\text{Number of Rolls of 1}}{\text{Total Rolls}}
\]
\[
\text{Experimental Probability} = \frac{14}{100} = 0.14
\]
2. **(b) Assuming that the cube is fair, compute the theoretical probability of rolling a 1.**
\[
\text{Theoretical Probability} = \frac{1}{6} \approx 0.167
\]
3. **(c) Assuming that the cube is fair, choose the statement below that is true:**
- \( \boxed{} \) As the number of rolls increases, we expect the experimental and theoretical probabilities to become closer, though they might not be equal.
- \( \boxed{} \) As the number of rolls increases, we expect the experimental and theoretical probabilities to become farther apart.
- \( \boxed{} \) The experimental and theoretical probabilities must always be equal.
### Explanation
In the given problem, Mary rolled a cube and recorded the number of times each outcome occurred. The table above summarizes her results.
To find the **experimental probability** of rolling a 1, we divide the number of times 1 was rolled by the total number of rolls:
\[
\frac{14}{100} = 0.14
\]
The **theoretical probability** assumes that the cube is fair. Therefore, the probability of rolling any single number (e.g., a 1) is:
\[
\frac{1}{6} \approx 0.167
\]
We also consider the nature of probability. If a cube is fair, as the number of rolls increases, the experimental probability
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