This is a bit more difficult probability puzzle. Old classics, fun to solve, if you haven’t encountered a similar problem before.
As a young aspiring Chief Statistician at the King’s Court, you are presented with this challenge. You must select a bride with the largest dowry. (Being married is a requirement for the Chief Statistician position.) Wherefore, you must choose from 100 equally beautiful young females with a weakness for only the smartest of statisticians, where each bride’s family offers a different dowry. The $ amount of each dowry is written on the backside of the girl’s personal card. Those amounts are presented to you one at a time in random order. When an amount is presented to you, you may either reject it, or settle for it. When you reject a dowry, you are presented the next card. If you fail to choose the dowry, which is the largest among 100, then you loose both your chance for the Court position and your right to claim your bride.
What strategy can you develop to maximize your chance for the position and the wealthy bride? What is the best chance?
(Obviously, the dowries are presented to you just once -- no chance of going back to the amount you’ve rejected. The range of the dowries is unknown.)