Problem 2. (20 points) I am trying to send you a single bit, either a 0 or a 1. When I transmit the bit, it goes through a series of n relays before it arrives to you. Each relay flips the bit independently with probability p. (a) Argue that the probability you receive the correct bit is [n/2] [ ( 21 ) 1 2 ( 1 - 2) m - 24 Be sure to explain your work. (b) We consider an alternative way to calculate this probability. Let us say the relay has bias q if the probability it flips the bit is (1- q)/2. The bias q is therefore a real number in the range [-1, 1]. Prove that sending a bit through two relays with bias q1 and q2 is equivalent to sending a bit through a single relay with bias q192. (c) Using part (b), prove that the probability you receive the correct bit when it passes through n relays as described in (a) is 1+ (1-2p)" 2