Q: You have two urns and 100 marbles, 50 white and 50 black. You wish to maximize the odds that someone picking a marble at random from one of the urns will pick a black marble. How do you do so, and what are the maximum odds?
A: Put one black marble in one urn, and all the other marbles in the other urn. Then the person will have a 1 in 2 chance of picking the urn with the single black marble, and a 1 in 2 chance of picking the urn containing 49 black marbles out of 99. This gives a combined odds of 148 : 198 or 74 : 99 or a little under 3 : 4 of picking a black marble.