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Topic: Can we help this guy to maximize chance of winning (Read 1386 times) |
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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!
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| « Last Edit: Apr 1st, 2008, 2:56am by wonderful » |
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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? |
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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). 
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temporary
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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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Hippo
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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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towr
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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 |
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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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Hippo
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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). |
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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). 
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| « Last Edit: Apr 3rd, 2008, 7:28am by Hippo » |
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