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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
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
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._
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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