Question

The king to test a candidate for the position of wise man, offers him a chance to marry the young lady in the court with the largest dowry. The amounts of the dowries are written on slips of paper and mixed. A slip is drawn at random and the wise man must decide whether that is the largest dowry or not, If he decides it is, he gets the lady and her dowry if he is correct; otherwise he gets nothing. If he decides against the amount written on the first slip, he must choose or refuse the next slip, and so until he chooses one or else the slips are exhausted. In all, 100 attractive young ladies participates, each with a different dowry how should the wise man make his decision.

Answer 1

This mathematics problem is best approached using the 'Secretary Problem' strategy, which involves a sample-and-decide phase to maximize the probability of choosing the largest dowry.

Step-by-step explanation:

The scenario presented involves a mathematical strategy problem, where a wise man must decide the most optimal strategy to pick the largest dowry. This falls under the umbrella of probability theory and decision-making which is categorically a mathematical subject matter.

The optimal strategy is known as the 'Secretary Problem' or 'Marriage Problem' in mathematics. To maximize his chances, the wise man should follow a sample-and-decide approach.

He should initially pass over a certain number of dowries (the sample phase) e.g. the first 37% of the total dowries, and then choose the next dowry that is larger than all the ones he has seen so far (the decision phase). This strategy is based on the theory that gives the highest probability, about 1/e (where e is the base of natural logarithms, approximately 2.718), of choosing the largest dowry.

By initially passing over approximately the first 37% of dowries and then selecting the next dowry larger than all previously seen, the wise man improves his odds of success.