I like the Secretary problem:
The basic form of the problem is the following: imagine an administrator who wants to hire the best secretary out of n rankable applicants for a position. The applicants are interviewed one by one in random order. A decision about each particular applicant is to be made immediately after the interview. Once rejected, an applicant cannot be recalled. During the interview, the administrator gains information sufficient to rank the applicant among all applicants interviewed so far, but is unaware of the quality of yet unseen applicants. The question is about the optimal strategy (stopping rule) to maximize the probability of selecting the best applicant.
Have a look at these articles for details:
- Secretary problem – Wikipedia
- Math-Based Decision Making: The Secretary Problem | by Lorenzo Duso | Cantor’s Paradise
- Secretary Problem (A Optimal Stopping Problem) – GeeksforGeeks
- The Secretary Problem
