RB_CH04_Q015. Two jars 100 marbles blindfolded

You are presented with two empty jars and 100 marbles on a table. There are 50 white marbles and 50 black marbles. You will then put all 100 of the marbles into the two jars in any way you choose. I will then blindfold you. I will shake the jars up to ensure good mixing, and I will rearrange the placing of the jars on the table so that you do not know which one is which. You may then request either the 'left-hand' or the 'right-hand' jar. You get to choose exactly one jar, you are allowed to withdraw at most one marble from the jar, and you do not get a second choice if you are unhappy with your choice. How many of each color marble should you place in each jar to maximize the probability that your blindfolded random draw obtains a white marble?