An article in the Transportation Research Part E Journal [Arc Routing Problems to Restore Connectivity of a Road Network" (2016)] considered ways of re-establishing the connectivity of road networks after a natural disaster-earthquake. Estimates. of the probabilities of a randomly chosen road being under light debris, moderate debris, and heavy debris conditions after different disaster magnitudes are shown in the following table. Disaster magnitude is equally likely to be low, moderate or high. OYes, because P(ANB) P(A) P(B) OYes, because P(ANB)=P(A) P(B) O No, because P(ANB)=P(A) P(B) O No, because Disaster Magnitude P(ANB) P(A) P(B) Low Moderate High Total Let A and B denote the events that the earthquake magnitude is high and the road debris is moderate. Are these events independent? Light Moderate Heavy Total Debris Debris Debris 5 100 10 100 100 35 300 80 50 30 160 15 40 50 105 20
An article in the Transportation Research Part E Journal [Arc Routing Problems to Restore Connectivity of a Road Network" (2016)] considered ways of re-establishing the connectivity of road networks after a natural disaster-earthquake. Estimates. of the probabilities of a randomly chosen road being under light debris, moderate debris, and heavy debris conditions after different disaster magnitudes are shown in the following table. Disaster magnitude is equally likely to be low, moderate or high. OYes, because P(ANB) P(A) P(B) OYes, because P(ANB)=P(A) P(B) O No, because P(ANB)=P(A) P(B) O No, because Disaster Magnitude P(ANB) P(A) P(B) Low Moderate High Total Let A and B denote the events that the earthquake magnitude is high and the road debris is moderate. Are these events independent? Light Moderate Heavy Total Debris Debris Debris 5 100 10 100 100 35 300 80 50 30 160 15 40 50 105 20
MATLAB: An Introduction with Applications
6th Edition
ISBN:9781119256830
Author:Amos Gilat
Publisher:Amos Gilat
Chapter1: Starting With Matlab
Section: Chapter Questions
Problem 1P
Related questions
Question
100%
![An article in the *Transportation Research Part E Journal* [“Arc Routing Problems to Restore Connectivity of a Road Network” (2016)] considered ways of re-establishing the connectivity of road networks after a natural disaster—earthquake. Estimates of the probabilities of a randomly chosen road being under light debris, moderate debris, and heavy debris conditions after different disaster magnitudes are shown in the following table. Disaster magnitude is equally likely to be low, moderate or high.
| Disaster Magnitude | Light Debris | Moderate Debris | Heavy Debris | Total |
|---------------------|--------------|----------------|--------------|-------|
| Low | 80 | 15 | 5 | 100 |
| Moderate | 50 | 40 | 10 | 100 |
| High | 30 | 50 | 20 | 100 |
| Total | 160 | 105 | 35 | 300 |
Let \( A \) and \( B \) denote the events that the earthquake magnitude is high and the road debris is moderate. Are these events independent?
- O Yes, because \( P(A \cap B) \ne P(A)P(B) \)
- O Yes, because \( P(A \cap B) = P(A)P(B) \)
- O No, because \( P(A \cap B) = P(A)P(B) \)
- O No, because \( P(A \cap B) \ne P(A)P(B) \)](/v2/_next/image?url=https%3A%2F%2Fcontent.bartleby.com%2Fqna-images%2Fquestion%2F032f9f2f-4a86-4f7c-abbd-a161821f35fd%2F5f95013d-b6c2-4510-b46e-71f521f505b5%2F8xv9t9_processed.jpeg&w=3840&q=75)
Transcribed Image Text:An article in the *Transportation Research Part E Journal* [“Arc Routing Problems to Restore Connectivity of a Road Network” (2016)] considered ways of re-establishing the connectivity of road networks after a natural disaster—earthquake. Estimates of the probabilities of a randomly chosen road being under light debris, moderate debris, and heavy debris conditions after different disaster magnitudes are shown in the following table. Disaster magnitude is equally likely to be low, moderate or high.
| Disaster Magnitude | Light Debris | Moderate Debris | Heavy Debris | Total |
|---------------------|--------------|----------------|--------------|-------|
| Low | 80 | 15 | 5 | 100 |
| Moderate | 50 | 40 | 10 | 100 |
| High | 30 | 50 | 20 | 100 |
| Total | 160 | 105 | 35 | 300 |
Let \( A \) and \( B \) denote the events that the earthquake magnitude is high and the road debris is moderate. Are these events independent?
- O Yes, because \( P(A \cap B) \ne P(A)P(B) \)
- O Yes, because \( P(A \cap B) = P(A)P(B) \)
- O No, because \( P(A \cap B) = P(A)P(B) \)
- O No, because \( P(A \cap B) \ne P(A)P(B) \)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
This is a popular solution!
Trending now
This is a popular solution!
Step by step
Solved in 3 steps
Follow-up Questions
Read through expert solutions to related follow-up questions below.
Follow-up Question
| Disaster Magnitude | Light Debris | Moderate Debris | Heavy Debris | Total |
| Low | 80 | 15 | 5 | 100 |
| Moderate | 50 | 40 | 10 | 100 |
| High | 30 | 50 | 20 | 100 |
| Total | 160 | 105 | 35 | 300 |
Given that a road had heavy debris after an earthquake , what is the conditional probability that the disaster magnitude was high ?
Solution
by Bartleby ExpertRecommended textbooks for you
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
MATLAB: An Introduction with Applications
Statistics
ISBN:
9781119256830
Author:
Amos Gilat
Publisher:
John Wiley & Sons Inc
Probability and Statistics for Engineering and th…
Statistics
ISBN:
9781305251809
Author:
Jay L. Devore
Publisher:
Cengage Learning
Statistics for The Behavioral Sciences (MindTap C…
Statistics
ISBN:
9781305504912
Author:
Frederick J Gravetter, Larry B. Wallnau
Publisher:
Cengage Learning
Elementary Statistics: Picturing the World (7th E…
Statistics
ISBN:
9780134683416
Author:
Ron Larson, Betsy Farber
Publisher:
PEARSON
The Basic Practice of Statistics
Statistics
ISBN:
9781319042578
Author:
David S. Moore, William I. Notz, Michael A. Fligner
Publisher:
W. H. Freeman
Introduction to the Practice of Statistics
Statistics
ISBN:
9781319013387
Author:
David S. Moore, George P. McCabe, Bruce A. Craig
Publisher:
W. H. Freeman