Barbara is interviewing 8 candidates for a position. As she interviews candidates, she can determine their relative rank but not their true rank. For example, if there are 5 candidates and their true rank is 4, 2, 5, 1, 3 and she has interviewed the first three, she would rank them 2, 1, 3. She interviews the candidates one at a time, and after each interview she must either offer the candidate the position or reject them. Once she rejects a candidate they are lost forever. She wants to decide on a strategy for deciding when to stop and accept a candidate that will maximize the probability that she gets the best candidate. Assume the candidates arrive in random order. Suppose the interviewer adopts the following strategy. She rejects the first 6 candidates. If the second to last candidate is better than all of the previous 6 candidates, then she chooses that candidate. Otherwise, she chooses the last candidate. What is the probability that she gets the best candidate with this strategy?

Barbara is interviewing 8 candidates for a position. As she interviews candidates, she can determine their relative rank but not their true rank. For example, if there are 5 candidates and their true rank is 4, 2, 5, 1, 3 and she has interviewed the first three, she would rank them 2, 1, 3. She interviews the candidates one at a time, and after each interview she must either offer the candidate the position or reject them. Once she rejects a candidate they are lost forever. She wants to decide on a strategy for deciding when to stop and accept a candidate that will maximize the probability that she gets the best candidate. Assume the candidates arrive in random order. Suppose the interviewer adopts the following strategy. She rejects the first 6 candidates. If the second to last candidate is better than all of the previous 6 candidates, then she chooses that candidate. Otherwise, she chooses the last candidate. What is the probability that she gets the best candidate with this strategy?

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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