The Secretary Problem
You interview n candidates sequentially. After each interview you must immediately accept or reject; you cannot go back. Using the optimal stopping rule (reject the first n/e candidates, then hire the next one who is better than all previous), what is the probability of hiring the best candidate as n → ∞? Express your answer as a fraction or decimal rounded to 4 decimal places.
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Source: The secretary problem, popularised by Martin Gardner in Scientific American (1960); solved by Dennis Lindley (1961). Statement written for AxiomIQ.