Suppose Joe is seeking a job. He decides to consider n possible jobs. However, after being offered a job, he must immediately decide whether to accept it or decline it and consider the next job that becomes available Notice that when considering a new job offer Joe only knows the relative rank of that job

Elements Of Modern Algebra
8th Edition
ISBN:9781285463230
Author:Gilbert, Linda, Jimmie
Publisher:Gilbert, Linda, Jimmie
Chapter1: Fundamentals
Section1.5: Permutations And Inverses
Problem 3E
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Suppose Joe is seeking a job. He decides to
consider n possible jobs. However, after
being offered a job, he must immediately
decide whether to accept it or decline it and
consider the next job that becomes available
Notice that when considering a new job offer
Joe only knows the relative rank of that job
compared to the ones he has already
declined. Assume that all n! orderings are
equally likely and that once a job is declined i
is gone forever. Suppose Joe's strategy is to
reject the first k jobs and then accept the first
one that is better than all of those first k.
a For a given value of k, what is the
probability that Joe selects the best job?
b What value of k would maximize the
probability that Joe selects the best job
under this strategy?
Transcribed Image Text:Suppose Joe is seeking a job. He decides to consider n possible jobs. However, after being offered a job, he must immediately decide whether to accept it or decline it and consider the next job that becomes available Notice that when considering a new job offer Joe only knows the relative rank of that job compared to the ones he has already declined. Assume that all n! orderings are equally likely and that once a job is declined i is gone forever. Suppose Joe's strategy is to reject the first k jobs and then accept the first one that is better than all of those first k. a For a given value of k, what is the probability that Joe selects the best job? b What value of k would maximize the probability that Joe selects the best job under this strategy?
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