You are preparing to begin the process of hiring a new employee for your company. Four candidates have applied for the position and arrive to be interviewed one at a time, in a random order. Your supervisor imposes the following restrictions that your hiring committee must follow:
You have no prior knowledge about the quality of any of the candidates. In other words, after you have interviewed a candidate, you have no idea how they compare to the other candidates still waiting to be interviewed.
After interviewing a candidate, you must immediately decide whether to hire that person.
If you decide to hire them, the hiring process ends and all other candidates are politely declined.
Otherwise, the process continues, and you can no longer consider hiring that candidate (possibly because another competitor has already snatched them up!)
Your supervisor will only be satisfied if you hire the very best candidate.
Let’s use the following number system for the candidates:
Candidate 1 is the best candidate.
Candidate 2 is the second best candidate.
Candidate 3 is the third best candidate.
Candidate 4 is the worst candidate.
a. List all possible orderings for the interviews.
Table 5 Interview Orderings
b. What is the probability that you successfully hire the best candidate on the first try?
One of your colleagues on the hiring committee says he read some research that suggests that the chance of hiring the best candidate will be higher if you let the first candidate go by, and then hire the next candidate you see who is the best so far. List all orderings that result in successfully hiring the best candidate using this method, then find the corresponding probability.
Another colleague suggests letting the first two candidates go by, and then hiring the next candidate you see who is the best so far. List all orderings that result in successfully hiring the best candidate using this method, then find the corresponding probability.
Which is the optimal hiring strategy hiring the first candidate, letting one candidate go by, or letting two candidates go by? Why?
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