An employer is about to hire one new employee from a group of N candidates, whose future potential can be rated on a scale from I to N. The employer proceeds according to the following rules: (a) Each candidate is seen in succession (in random order) and a decision is made whether to hire the candidate. (b) Having rejected m-1 candidates (m > 1), the employer can hire the mth candidate only if the mth candidate is better than the previous m - 1. Suppose a candidate is hired on the ith trial. What is the probability that the best candidate was hired?

Advanced Engineering Mathematics
10th Edition
ISBN:9780470458365
Author:Erwin Kreyszig
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An employer is about to hire one new employee from a group of N candidates, whose
future potential can be rated on a scale from I to N. The employer proceeds according
to the following rules:
(a) Each candidate is seen in succession (in random order) and a decision is made
whether to hire the candidate.
(b) Having rejected m-1 candidates (m > 1), the employer can hire the mth candidate
only if the mth candidate is better than the previous m - 1.
Suppose a candidate is hired on the ith trial. What is the probability that the best
candidate was hired?
Transcribed Image Text:An employer is about to hire one new employee from a group of N candidates, whose future potential can be rated on a scale from I to N. The employer proceeds according to the following rules: (a) Each candidate is seen in succession (in random order) and a decision is made whether to hire the candidate. (b) Having rejected m-1 candidates (m > 1), the employer can hire the mth candidate only if the mth candidate is better than the previous m - 1. Suppose a candidate is hired on the ith trial. What is the probability that the best candidate was hired?
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