Even Cooler Problem Involving e

[David Sklansky]

There is a bunch of woman at a party. You are not invited. But you have some enticements in your pocket that is guaranteed to get any one of them to go home with you.

Your plan is to approach one as she leaves. You know that they will leave one by one. You know how many ladies are at the party. You hope to pick the prettiest. Your strategy is to let a certain number of girls walk past you (all of whom you see perfectly) and then pick the first girl you consider prettier than any of the ones you let go by. Of course if the prettiest girl at the party is in the first group, you are out of luck, and are stuck with the last girl. (Once any girl passes she is gone.)

The question is "if the number of girls at the party is n, what are the chances you go home with the prettiest one?"

But before the mathmeticians here answer that question, please let the non mathmeticians ESTIMATE the answer to this second question:

If you were told the answer to the question when the number of girls at the party was 100, and you were asked to answer the question if the number of girls was 10,000, you would take the solution for 100 and divide it by about what? In other words how much more unlikely would it be that you would succeed with 10,000 vs 100 at the party?