You play the following game against your friend. You have two urns and three balls. One of the balls is marked. You get to place the balls in the two urns any way you please, including leaving one urn empty. Your friend will choose one urn at random and then draw a ball from that urn. (If he chose an empty urn, there is no ball.) His goal is to draw the marked ball. (a) How would you arrange the balls in the urns to minimize his chances of drawing the marked ball? (b) How would your friend arrange the balls in the urns to maximize his chances of drawing the marked ball? (c) Repeat (a) and (b) for the case of n balls with one marked ball.