Suppose we have $n$ blocks of wood. At each step, we choose one of these boxes uniformly at random and paint it red (so at later steps, we may be re-painting an already-red box). Let $X_t$ denote the percentage of the boxes painted red at time $t$.
In other words, take $X_0 = 0$ and let
$X_{t+1} = \begin{cases} X_t & \text{ with probability } X_t \\ X_t + 1/n & \text{ with probability } 1 - X_t \end{cases}$
Question: What is the name of this process?