July 15, 2008

Of Marbles, Jars and Life

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)

Ans - Put one white marble in one jar and put all the other white marbles in the other jar.
Probability of white getting selected - 1/2(1) + 1/2(49/99) roughly = 3/4

8 comments:

Alistair D'souza said...

so you're been giving some exams :-)

Eliza said...

No that is due to my puzzleholic husband :p

Mridul said...
This comment has been removed by the author.
Mridul said...

feel really foolish to have posted prev comment ... removing it :-)

Anonymous said...

are u sure about the answer...it says each jar shud have 1 ball of eachcolor...

Anonymous said...

Amiable dispatch and this enter helped me alot in my college assignement. Gratefulness you as your information.

kalyan said...

in the question, it was clearly mentioned that marbles can only be swaped. it means finally both jars must contain 50 marbles

kalyan said...

so finally total probability remains 0.5 always