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        riddles >> hard >> Can we help this guy to maximize chance of winning
        
(Message started by: wonderful on Apr 1^st, 2008, 2:55am)

Title: Can we help this guy to maximize chance of winning
Post by wonderful on Apr 1^st, 2008, 2:55am

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!

Title: Re: Can we help this guy to maximize chance of win
Post by Grimbal on Apr 1^st, 2008, 2:59am

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.

Title: Re: Can we help this guy to maximize chance of win
Post by towr on Apr 1^st, 2008, 3:37am

on 04/01/08 at 02:55:45, 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; [hide]put a single white marble in one box, the rest of the marbles in the other[/hide]

[hide]And then she pick the box randomly proportional to weight, and a marble uniformly random from the black marbles (if there is one).[/hide] ;)

Title: Re: Can we help this guy to maximize chance of win
Post by temporary on Apr 1^st, 2008, 4:45pm

You were right about the [hide]1 white marble in 1 box, 99 white and 100 black in the other[/hide], but how does that have anything to do with her picking one randomly based on weight.

Title: Re: Can we help this guy to maximize chance of win
Post by Hippo on Apr 1^st, 2008, 11:58pm

temp: Let it be, [hide]he is just joking[/hide]

Title: Re: Can we help this guy to maximize chance of win
Post by towr on Apr 2^nd, 2008, 12:48am

on 04/01/08 at 23:58:13, Hippo wrote:

temp: Let it be, [hide]he is just joking[/hide]

Well, not entirely; we don't know the princess's random process for picking a marble; it needn't be uniform at either stage.

Title: Re: Can we help this guy to maximize chance of win
Post by Hippo on Apr 3^rd, 2008, 7:27am

on 04/01/08 at 03:37:50, towr wrote:

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

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). ;D