The real mathematics:
Let O_best function as the arrival purchase of this most useful prospect (Mr/Mrs. Ideal, The One, X, the candidate whoever ranking is 1, etc.) We don’t know whenever this individual will get to our life, but we realize for certain that from the next, pre-determined N people we will see, X will show up at purchase O_best = i.
Let S(n,k) function as the occasion of success in selecting X among N prospects with this technique for M = k, that is, checking out and categorically rejecting the k-1 that is first, then settling utilizing the very very very first individual whose ranking is preferable to all you’ve got seen to date. We are able to observe that:
Exactly why is it the actual situation? It’s apparent that if X is amongst the very first k-1 people who enter our life, then regardless of whom we choose later, we can not perhaps choose X (even as we consist of X in people who we categorically reject). Otherwise, into the 2nd situation, we realize that our strategy can simply be successful if one associated with the very very first k-1 individuals is the better one of the primary i-1 people.