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information, what should they believe the probability they are winning is?

information, what should they believe the probability they are winning is?

A First Course in Probability (10th Edition)
A First Course in Probability (10th Edition)
10th Edition
ISBN:9780134753119
Author:Sheldon Ross
Publisher:Sheldon Ross
Chapter1: Combinatorial Analysis
Section: Chapter Questions
Problem 1.1P: a. How many different 7-place license plates are possible if the first 2 places are for letters and...
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A political candidate is trying to determine the state of the race. Based on prior information, they believe that there is a 70% chance that they are ahead. They commission a new poll. This poll has an 80% chance of correctly identifying who is ahead. So, if the candidate is in fact ahead, the poll would show they are ahead 80% of the time, and behind 20% of the time. Conversely, if the candidate is behind, the poll would show they are ahead 20% of the time and behind 80% of the time. The new poll shows that contrary to prior information, the candidate is losing the race. Given all this information, what should they believe the probability they are winning is?
Transcribed Image Text:A political candidate is trying to determine the state of the race. Based on prior information, they believe that there is a 70% chance that they are ahead. They commission a new poll. This poll has an 80% chance of correctly identifying who is ahead. So, if the candidate is in fact ahead, the poll would show they are ahead 80% of the time, and behind 20% of the time. Conversely, if the candidate is behind, the poll would show they are ahead 20% of the time and behind 80% of the time. The new poll shows that contrary to prior information, the candidate is losing the race. Given all this information, what should they believe the probability they are winning is?
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