[DISCRETE MATH]

Consider a coin that comes up heads with probability 1/3 and, thus, tails with probability 2/3. Consider the following recursive algorithm Heads, which takes as input a positive integer k: Algorithm Heads(k)://all coin flips made are mutually independent flip the coin; if the coin came up heads then return k + 1 else Heads(k + 1) endif You run algorithm Heads(1), i.e., with k = 1. Define the random variable X to be the value of the output of this algorithm. Let m greaterthanorequalto 1 be an integer. What is Pr(X = m + 1)? (a) 2^m - 1/3^m (b) (2/3)^m (c) 2^m/3^m + 1 (d) (2/3)^m + 1