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   Can we help this guy to maximize chance of winning
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   Author  Topic: Can we help this guy to maximize chance of winning  (Read 1370 times)
wonderful
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Can we help this guy to maximize chance of winning  
« on: Apr 1st, 2008, 2:55am »
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Once upon a time, a lovely princess in response to a proposal from a guy saying that she would married him under the following condition:
 
There are 100 white marbles and 100 black marbles. The guy then disbutes these marbles to two different boxes. The princess then randomly choose a box and randomly pick a marble from that chosen box. She would marry the guy if the marble she picked was white marble.
 
Can you help the guy to  maximize the chance of winning?
 
Have A Great Day!
« Last Edit: Apr 1st, 2008, 2:56am by wonderful » IP Logged
Grimbal
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Re: Can we help this guy to maximize chance of win  
« Reply #1 on: Apr 1st, 2008, 2:59am »
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The question has been seen on this forum before, of course.
 
You could put all white marbles in one box and all black marbles in the other box, with a big ugly spider.
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towr
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Re: Can we help this guy to maximize chance of win  
« Reply #2 on: Apr 1st, 2008, 3:37am »
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on Apr 1st, 2008, 2:55am, wonderful wrote:
Can you help the guy to  maximize the chance of winning?
Sometimes the best way to win is not to play. Can you imagine being married to someone who makes every life changing decision into a game?
 
Oh fine; put a single white marble in one box, the rest of the marbles in the other
 
And then she pick the box randomly proportional to weight, and a marble uniformly random from the black marbles (if there is one). Wink
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Re: Can we help this guy to maximize chance of win  
« Reply #3 on: Apr 1st, 2008, 4:45pm »
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You were right about the 1 white marble in 1 box, 99 white and 100 black in the other, but how does that have anything to do with her picking one randomly based on weight.
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Re: Can we help this guy to maximize chance of win  
« Reply #4 on: Apr 1st, 2008, 11:58pm »
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temp: Let it be, he is just joking
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Re: Can we help this guy to maximize chance of win  
« Reply #5 on: Apr 2nd, 2008, 12:48am »
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on Apr 1st, 2008, 11:58pm, Hippo wrote:
temp: Let it be, he is just joking
Well, not entirely; we don't know the princess's random process for picking a marble; it needn't be uniform at either stage.
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Re: Can we help this guy to maximize chance of win  
« Reply #6 on: Apr 3rd, 2008, 7:27am »
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on Apr 1st, 2008, 3:37am, towr wrote:

And a marble uniformly random from the black marbles (if there is one). Wink

 
This is what I expected was a joke.  
I would let her to continue with a marble uniformly random from the box. This sets his chances to 1/2 what is big improvement from 1/199. (But of course for your princess the solution is to put white marbles in one and black to the other to got 1/2 as well). Grin
« Last Edit: Apr 3rd, 2008, 7:28am by Hippo » IP Logged
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