Calculate the relative frequency P(E) using the given information. (Round your answer to two decimal places.) A die is rolled 70 times with the following result: 1 and 2 never come up, 3 and 4 each come up 15 times, and 5 and 6 each come up 20 times. E is the event that the number that comes up is at least 4. P(E) =
Calculate the relative frequency P(E) using the given information. (Round your answer to two decimal places.) A die is rolled 70 times with the following result: 1 and 2 never come up, 3 and 4 each come up 15 times, and 5 and 6 each come up 20 times. E is the event that the number that comes up is at least 4. P(E) =
MATLAB: An Introduction with Applications
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ISBN:9781119256830
Author:Amos Gilat
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Chapter1: Starting With Matlab
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![**Title: Calculating Relative Frequency of a Die Roll Event**
**Problem Statement:**
Calculate the relative frequency \( P(E) \) using the given information. (Round your answer to two decimal places.)
A die is rolled 70 times with the following result:
- Numbers 1 and 2 never come up.
- Numbers 3 and 4 each come up 15 times.
- Numbers 5 and 6 each come up 20 times.
**Event Definition:**
\( E \) is the event that the number that comes up is at least 4.
**Calculation:**
The numbers that are at least 4 are 4, 5, and 6. Here are the occurrences:
- Number 4 comes up 15 times.
- Number 5 comes up 20 times.
- Number 6 comes up 20 times.
**Total occurrences of numbers at least 4:**
\[ 15 + 20 + 20 = 55 \]
**Total number of rolls:**
\[ 70 \]
**Relative frequency of event \( E \):**
\[ P(E) = \frac{\text{Number of successful outcomes}}{\text{Total outcomes}} = \frac{55}{70} \]
This computes to approximately:
\[ P(E) = 0.79 \]
\[ \therefore \, P(E) = 0.79 \]
_Explanation: The relative frequency is calculated by dividing the number of times the event occurs by the total number of trials and rounding the result to two decimal places._](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F130466a8-d623-4a36-8d8e-5f52db48e11b%2F39f87288-3ec9-48c9-8a64-982352729c1d%2F6s7ed4e_processed.png&w=3840&q=75)
Transcribed Image Text:**Title: Calculating Relative Frequency of a Die Roll Event**
**Problem Statement:**
Calculate the relative frequency \( P(E) \) using the given information. (Round your answer to two decimal places.)
A die is rolled 70 times with the following result:
- Numbers 1 and 2 never come up.
- Numbers 3 and 4 each come up 15 times.
- Numbers 5 and 6 each come up 20 times.
**Event Definition:**
\( E \) is the event that the number that comes up is at least 4.
**Calculation:**
The numbers that are at least 4 are 4, 5, and 6. Here are the occurrences:
- Number 4 comes up 15 times.
- Number 5 comes up 20 times.
- Number 6 comes up 20 times.
**Total occurrences of numbers at least 4:**
\[ 15 + 20 + 20 = 55 \]
**Total number of rolls:**
\[ 70 \]
**Relative frequency of event \( E \):**
\[ P(E) = \frac{\text{Number of successful outcomes}}{\text{Total outcomes}} = \frac{55}{70} \]
This computes to approximately:
\[ P(E) = 0.79 \]
\[ \therefore \, P(E) = 0.79 \]
_Explanation: The relative frequency is calculated by dividing the number of times the event occurs by the total number of trials and rounding the result to two decimal places._
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