BT 1: ProbabilityYou have 100 marbles: 50 black marbles and 50 white marbles. You have two buckets. You have a blindfolded contestant who is going to pick one marble from one of the buckets -- the bucket is chosen at random and the marble is chosen from that bucket at random.
Your challenge is to put the marbles into the buckets in such a way that you maximize the probability the contestant picks a black marble. You must use all the marbles.