Homework Help is Here – Start Your Trial Now!
Math
Probability
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)
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...
See similar textbooks
icon
Related questions
Question

Need help with probability

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?
Transcribed Image Text: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?
Expert Solution
steps

Step by step

Solved in 3 steps with 2 images

SEE SOLUTIONCheck out a sample Q&A here
Blurred answer