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DOWRY


Best Answer bushindo, 08 January 2013 - 08:27 PM

Okay, second time is the charm,

 

Spoiler for equations
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14 replies to this topic

#1 Prime

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Posted 08 January 2013 - 03:21 AM

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.)


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Past prime, actually.


#2 bushindo

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Posted 08 January 2013 - 04:12 AM

Here's an approach,

Spoiler for


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#3 vistaptb

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Posted 08 January 2013 - 04:13 AM

Spoiler for Seen this one before


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#4 Prime

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Posted 08 January 2013 - 04:41 AM

Spoiler for Seen this one before

I did stipulate that it would be fun to solve if you haven't encountered a similar problem before. If you remember seeing such problem but have forgotten the solution (as seems to be the case,) it could be fun to derive and prove it over again.


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Past prime, actually.


#5 bushindo

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Posted 08 January 2013 - 04:43 AM

Here's an approach,

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Forgot about some cases in computation of winning chance. Back to the drawing board.


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#6 Caliban27

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Posted 08 January 2013 - 07:17 AM

Spoiler for stats


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#7 Prime

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Posted 08 January 2013 - 08:19 AM

Spoiler for stats

The range of dowry amounts is unknown. There is no average, no deviation.


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Past prime, actually.


#8 bonanova

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Posted 08 January 2013 - 11:06 AM

This puzzle asks for the strategy that maximizes the likelihood of choosing the babe with the greatest dowry.

 

Real-life situations often ask for the strategy that yields the best result, on average - best result or not.

Clearly a strategy that on average gets you into the top ten percent of the dowries would be preferred over

one has a better shot at picking the highest dowry but on average gets you only into the top twenty percent.

 

That said, and if someone has written the simulation for this puzzle, I wonder where the OP best strategy

places you in the distribution, on average. And, is there a strategy that places you higher?

 

A good sample set of dowries to find out would be simply 1, 2, 3, ... , 98, 99, 100. Run the algorithm

100,000 times without using knowledge of the distribution, and average the value of the result. 


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The greatest challenge to any thinker is stating the problem in a way that will allow a solution.
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#9 Rainman

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Posted 08 January 2013 - 06:53 PM

Spoiler for solution


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#10 bushindo

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Posted 08 January 2013 - 08:27 PM   Best Answer

Okay, second time is the charm,

 

Spoiler for equations

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