2. A certain calculating machine uses only the digits 0 and 1. It is supposed to transmit one of these digits through several stages. However, at every stage, there is a probability 13 that the digit that enters this stage will be changed when it leaves and a probability (1 = 1 p that it won't. Form a Markov chain to represent the process of transmission by taking as states the digits 0 and 1. (a) Draw a diagram of this Markov chain. (b) Write the transmission probabilities as a matrix. (0) Suppose a digit starts in the state 0 and is transmitted twice. What is the probability that after these two transmissions it is 0 (i.e. correct)