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Blue Cab operates 15% of the taxis in a certain city, and

Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye ISBN: 9780321629111 32

Solution for problem 62E Chapter 2

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Probability and Statistics for Engineers and the Scientists | 9th Edition | ISBN: 9780321629111 | Authors: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye

Probability and Statistics for Engineers and the Scientists | 9th Edition

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Problem 62E

Blue Cab operates 15% of the taxis in a certain city, and Green Cab operates the other 85%. After a nighttime hit-and-run accident involving a taxi, an eyewitness said the vehicle was blue. Suppose, though, that under night vision conditions, only 80% of individuals can correctly distinguish between a blue and a green vehicle. What is the (posterior) probability that the taxi at fault was blue? In answering, be sure to indicate which probability rules you are using. [Hint: A tree diagram might help. Note: This is based on an actual incident.]

Step-by-Step Solution:

Answer Step 1 of 3 P(blue taxi)=P(B)=15%=0.15 P(green taxi)=P(G)=85%=0.85 P(witness saying blue when the cab is really blue)= P(SB|B) =0.80 P(witness saying green when the cab is really green)= P(SG|G) =0.80 the probabilities of misidentifications are: P(SG|B) =0.2 and P(SB|G) =0.2

Step 2 of 3

Chapter 2, Problem 62E is Solved
Step 3 of 3

Textbook: Probability and Statistics for Engineers and the Scientists
Edition: 9
Author: Ronald E. Walpole; Raymond H. Myers; Sharon L. Myers; Keying E. Ye
ISBN: 9780321629111

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Blue Cab operates 15% of the taxis in a certain city, and