Given 100 white marbles and 100 black marbles and two jaws. Put these marbles in the two jars in a way that would maximize the chance of retrieving a white marble from any given jaw.

Really that is what you would answer? What if they stirred the jars around after you distributed the marbles? Personally I think a better answer is to put 1 white marble in the first far and 99 white marbles and 100 black marbles in the second jar. If you choose the jar at random you now have a 74.87% chance of getting a white marble, regardless of the marbles position in the jar.

qq is right, that is the optimum combination.

2 colours, 2 jars. White in one, black in the other