4. [10 pts] Suppose you start with z = 1 and append digits to the end of z, each chosen mutually independently and uniformly at random from [0..9]. You repeat this process until z is even or z has 6 digits. What is the expected number of digits in z at the end of this process? For example, one possible instance of this process would be 117173 1731 17310, at which point the process stops because z = 17310 is even.