I was sitting warm and snug in my bed, full from Thanksgiving dinner and doing some reading for my Lit-A class (Dante). I suddenly leapt out of bed because I had a very bad feeling that I had a blog post due sometime right around now (in fact, yesterday). So, I’m very sorry for the delay…

The Secretary Problem is a pretty famous probability problem, introduced by Merrill M. Flood in 1949. It has a few other names, among them the marriage problem, the fiance problem, and the best choice problem. Here it is:

- There is a single secretarial position to fill.
- There are
*n* applicants for the position, and the value of *n* is known.
- The applicants can be ranked from best to worst with no ties.
- The applicants are interviewed sequentially in a random order, with each order being equally likely.
- After each interview, the applicant is accepted or rejected.
- The decision to accept or reject an applicant can be based only on the relative ranks of the applicants interviewed so far.
- Rejected applicants cannot be recalled.
- The object is to select the best applicant. The payoff is 1 for the best applicant and zero otherwise.

Click here for more information and the solution.

Interestingly, psychologists have conducted real-life experiments of the secretary problem, and people tend to stop searching too soon. Ah, a mathematical justification for a nonexistent dating life to the grandparents 🙂

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