1. For this problem, it will be very helpful to recall that for a real number x with |x| < 1, X n=0 x n = 1 1 x . Consider an experiment where we randomly select a positive integer. Our sample space is S = {1, 2, 3, . . . } and our probability function on S has the following values: P(n) = P({n}) = 1 2 n , for n = 2, 3, . . . . (a) Find P(1). (b) Let k S. Compute the probability the we select a number k. (c) Let k S. Compute the probability that we select a number k. (d) Compute the probability that we select an even number