Show clearly the steps and workings.

Consider the following recursive algorithm TWOTAILS, which takes as input a positive integer k: Algorithm TWOTAILS(A):/il coin flips made arc mutually independent flip a fair coin twice: if the coin came up heads exactly twice then return 2* else TWOTAILS(k + 1) endif You run algorithm TWOTAILS(1). i.e., with k = 1. Define the random variable X to be the value of the output of this algorithm. Let k greaterthanorequalto 1 be an integer. What is Pr(X = 2^k)? (a) (1/4)^k middot 3/4 (b) (1/4)^k-1 middot 3/4 (c) (3/4)^k middot 1/4 (d) (3/4)^k-1 middot 1/4 You repeatedly, and independently, roll two fair dice, until the sum of the values of the two dice is equal to 12. Define the random variable X to be the number of times you roll the pair of dice. What is the expected value of X? (a) 30 (b) 30 (c) 20 (d) 12