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 1 to N. The employer proceeds according to the following rules:
Each candidate is seen in succession (in random order) and a decision is made whether to hire the candidate.
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?