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?

Here use probability tree Define event and tree is in step 2

Answered: information, what should they believe…

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

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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Question

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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