10. A calculator has a display, which shows a nonnegative integer N, and a button, which replaces N by a random integer chosen uniformly from the set 10, 1,..., N-1,pro- vided that N>0. Initially, the display holds the number N= 2003. If the button is pressed repeatedly until N=0, what is the probability that the numbers 1, 10, 100 and 1000 will each show up on the display at some point?10. A calculator has a display, which shows a nonnegative integer N, and a button, which replaces N by a random integer chosen uniformly from the set {0, 1, . . . , N − 1}, pro￾vided that N > 0. Initially, the display holds the number N = 2003. If the button is pressed repeatedly until N = 0, what is the probability that the numbers 1, 10, 100, and 1000 will each show up on the display at some point? 2