I love this because I got it instantly and felt good :p
Enjoy.
you are a prisoner in a foreign land. your fate will be determined by a little game. there are two jars, one with 50 white marbles, and one with 50 black marbles. at this point, you are allowed to redistribute the marbles however you wish (e.g. swap a black marble with a white marble, etc.): the only requirement is that after you are done with the redistribution, every marble must be in one of the two jars. afterwards, both jars will be shaken up, and you will be blindfolded and presented with one of the jars at random. then you pick one marble out of the jar given to you. if the marble you pull out is white, you live; if black, you die. how should you redistribute the marbles to maximize the probability that you live; what is this maximum probability (roughly)?
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Dannyliu,
I think if you put any 50 marbles in each of the jars, you have always a 50% chance.
Your Example: 25 black, 25 white & 25 black, 25 white
Other combinations: Leave 50 black & 50 white
--> 50% chance to get the jar with the whites
10 black, 40 white & 40 black, 10 white
--> 50% chance to get a 80% chance plus
50% chance to get a 20% chance make 40%+10%=50%
and so on...
In my comment above it's
50% to get a 100% chance + 50% to get an almost 50% chance
Thats 75%...
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by: tijoePosted on 2003-01-02 at 05:49:28ID: 7655367
Put all marbles except for one white into one jar!
If they give you the jar with the one white, you are free.
If they give you the other, you have a chance of 49/99 to get free, which is almost 1/2. So the probability is roughly 3/4!