Riddle courtesy of William Wu’s riddle archive.

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. 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, and what is this maximum probability (roughly)?

i’ve heard a couple answers to this one.. i still think the best odds you can get overall is 50/50… someone suggested putting all the marbles exept one in one jar, and just one white marble in the other jar.. thus you get a 100% chance if you get the jar with just one marble, but then you have a 49% chance with the other jar.. doesn’t seem to really raise the odds in your favor, since the odds of you getting one jar over the other is still 50/50.. what do you think?

You can improve your chances to 75% in the way you describe (put all marbles but 1 white one in 1 jar).

You have a 50% chance of getting the jar with just one white marble. If you get that jar, you have a 100% chance of pulling the white jar. So you automatically get a 50% chance of living.

If you get the other jar, you still have almost a 50% chance of getting a white marble and living.

So your overall probability of living is:

Probability of getting jar 1 * probability of pulling a white marble from jar 1

+

Probability of getting jar 2 * probability of pulling a white marble from jar 2

=

0.50 * 1.00 + 0.50 * 0.50 = 0.5 + 0.25 = 0.75