wu :: forums « wu :: forums - Can we help this guy to maximize chance of winning » Welcome, Guest. Please Login or Register. Mar 25th, 2023, 6:24am RIDDLES SITE WRITE MATH! Home Help Search Members Login Register
 wu :: forums    riddles    hard (Moderators: Eigenray, ThudnBlunder, SMQ, Grimbal, william wu, towr, Icarus)    Can we help this guy to maximize chance of winning « Previous topic | Next topic »
 Pages: 1 Reply Notify of replies Send Topic Print
 Author Topic: Can we help this guy to maximize chance of winning  (Read 1329 times)
wonderful
Full Member

Posts: 203
 Can we help this guy to maximize chance of winning   « on: Apr 1st, 2008, 2:55am » Quote Modify

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
wu::riddles Moderator
Uberpuzzler

Gender:
Posts: 7523
 Re: Can we help this guy to maximize chance of win   « Reply #1 on: Apr 1st, 2008, 2:59am » Quote Modify

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.
 IP Logged
towr
wu::riddles Moderator
Uberpuzzler

Some people are average, some are just mean.

Gender:
Posts: 13730
 Re: Can we help this guy to maximize chance of win   « Reply #2 on: Apr 1st, 2008, 3:37am » Quote Modify

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).
 IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
temporary
Full Member

Posts: 255
 Re: Can we help this guy to maximize chance of win   « Reply #3 on: Apr 1st, 2008, 4:45pm » Quote Modify

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.
 IP Logged

My goal is to find what my goal is, once I find what my goal is, my goal will be complete.
Hippo
Uberpuzzler

Gender:
Posts: 919
 Re: Can we help this guy to maximize chance of win   « Reply #4 on: Apr 1st, 2008, 11:58pm » Quote Modify

temp: Let it be, he is just joking
 IP Logged
towr
wu::riddles Moderator
Uberpuzzler

Some people are average, some are just mean.

Gender:
Posts: 13730
 Re: Can we help this guy to maximize chance of win   « Reply #5 on: Apr 2nd, 2008, 12:48am » Quote Modify

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.
 IP Logged

Wikipedia, Google, Mathworld, Integer sequence DB
Hippo
Uberpuzzler

Gender:
Posts: 919
 Re: Can we help this guy to maximize chance of win   « Reply #6 on: Apr 3rd, 2008, 7:27am » Quote Modify

on Apr 1st, 2008, 3:37am, 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).
 « Last Edit: Apr 3rd, 2008, 7:28am by Hippo » IP Logged
 Pages: 1 Reply Notify of replies Send Topic Print

 Forum Jump: ----------------------------- riddles -----------------------------  - easy   - medium => hard   - what am i   - what happened   - microsoft   - cs   - putnam exam (pure math)   - suggestions, help, and FAQ   - general problem-solving / chatting / whatever ----------------------------- general -----------------------------  - guestbook   - truth   - complex analysis   - wanted   - psychology   - chinese « Previous topic | Next topic »