Imagine you are a deep sea diver in search of lost treasure. You have it on good authority that there is a shipwreck off the coast of Maryland, in one of three locations (call them A, B, and C). Based on historical records of sea routes, you estimate that there is an 78% probability the ship is at location A, a 15% probability that it is at location B, and a 7% probability that it is at location C. Unfortunately, visibility and other diving conditions vary widely among the locations, affecting your chances of uncovering treasure: in a single dive, you estimate that you have only a 5% chance of finding a shipwreck at location A, while you have a 70% chance of finding a shipwreck at location B, and an 80% chance of finding a shipwreck at location C. a) If you can only dive once, which location do you choose to maximize your chances of finding the shipwreck? b) Suppose you dive in your chosen location, and do not find the ship. How does this change the probabilities of the ship being in each location? c) You have a chance for one more dive. Where do you go to maximize your chances? (you can go back to the same location if you want, and the dive will be independent of the previous dive)
Imagine you are a deep sea diver in search of lost treasure. You have it on good authority that there is a shipwreck off the coast of Maryland, in one of three locations (call them A, B, and C). Based on historical records of sea routes, you estimate that there is an 78% probability the ship is at location A, a 15% probability that it is at location B, and a 7% probability that it is at location C. Unfortunately, visibility and other diving conditions vary widely among the locations, affecting your chances of uncovering treasure: in a single dive, you estimate that you have only a 5% chance of finding a shipwreck at location A, while you have a 70% chance of finding a shipwreck at location B, and an 80% chance of finding a shipwreck at location C. a) If you can only dive once, which location do you choose to maximize your chances of finding the shipwreck? b) Suppose you dive in your chosen location, and do not find the ship. How does this change the probabilities of the ship being in each location? c) You have a chance for one more dive. Where do you go to maximize your chances? (you can go back to the same location if you want, and the dive will be independent of the previous dive)
Practical Management Science
6th Edition
ISBN:9781337406659
Author:WINSTON, Wayne L.
Publisher:WINSTON, Wayne L.
Chapter2: Introduction To Spreadsheet Modeling
Section: Chapter Questions
Problem 20P: Julie James is opening a lemonade stand. She believes the fixed cost per week of running the stand...
Related questions
Question
Imagine you are a deep sea diver in search of lost treasure. You have it on good authority that there is a shipwreck off the coast of Maryland, in one of three locations (call them A, B, and C). Based on historical records of sea routes, you estimate that there is an 78% probability the ship is at location A, a 15% probability that it is at location B, and a 7% probability that it is at location C. Unfortunately, visibility and other diving conditions vary widely among the locations, affecting your chances of uncovering treasure: in a single dive, you estimate that you have only a 5% chance of finding a shipwreck at location A, while you have a 70% chance of finding a shipwreck at location B, and an 80% chance of finding a shipwreck at location C.
a) If you can only dive once, which location do you choose to maximize your chances of finding the shipwreck?
b) Suppose you dive in your chosen location, and do not find the ship. How does this change the probabilities of the ship being in each location?
c) You have a chance for one more dive. Where do you go to maximize your chances? (you can go back to the same location if you want, and the dive will be independent of the previous dive)
Expert Solution
This question has been solved!
Explore an expertly crafted, step-by-step solution for a thorough understanding of key concepts.
Step by step
Solved in 3 steps
Recommended textbooks for you
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Practical Management Science
Operations Management
ISBN:
9781337406659
Author:
WINSTON, Wayne L.
Publisher:
Cengage,
Operations Management
Operations Management
ISBN:
9781259667473
Author:
William J Stevenson
Publisher:
McGraw-Hill Education
Operations and Supply Chain Management (Mcgraw-hi…
Operations Management
ISBN:
9781259666100
Author:
F. Robert Jacobs, Richard B Chase
Publisher:
McGraw-Hill Education
Purchasing and Supply Chain Management
Operations Management
ISBN:
9781285869681
Author:
Robert M. Monczka, Robert B. Handfield, Larry C. Giunipero, James L. Patterson
Publisher:
Cengage Learning
Production and Operations Analysis, Seventh Editi…
Operations Management
ISBN:
9781478623069
Author:
Steven Nahmias, Tava Lennon Olsen
Publisher:
Waveland Press, Inc.