There is a bag full of balls numbered 1 to k. As you reach in to pick one, he notes that they are not all equally likely because of magic: ball 1 is least likely to be chosen, with probability c, where c is some constant. Ball 2 has probability 2c, Ball 3 has probability 3c, . . . , Ball k - 1 has probability (k - 1)c, and Ball k has probability kc. What is the expected value of the ball number you pick? Your answer can't use the constant c but will use k.