You have two urns and 100 marbles, 50 white and 50 black.

probability/gerrymander

Problem

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?

Show solution

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.

This is the principle behind gerrymandering of voting districts.