This was posed to me in an interview. I don’t know if there’s a “right” answer, or whether it’s just intended to probe the thinking process of the applicant.
You have 50 white marbles, 50 black marbles and two bags. Your task is to arrange the marbles in the bags so as to maximize the probability that a person making a blind selection from one of the bags will select a black marble.
My answer: Put one black marble in Bag 1, and the other 99 marbles in Bag 2. Each bag has a 50 percent chance of being selected. Bag 1 guarantees the selection of a black marble, while Bag 2 offers a probablility of almost 50 percent, so the overall probablility of selecting a black marble is slightly less than 75 percent.