Strange Dilution You have a jar of red marbles and blue marbles. At each time step, you draw a marble, and you note the color of the marble. Then, you dilute the proportion of the opposite-colored marbles by a factor of γ, where 0 < γ < 1. (For example: if you pick a red marble, then the proportion of blue marbles is reduced by a factor of γ.) If p is the fraction of marbles that started off as red, what is the expected proportion of red marbles at time n?