8. Hazel and Naomi each have a brown paper grocery bag containing three exotic fruits. Initially, Hazel's bag contains three persimmons and Naomi's bag contains three kumquats. Once every day, Hazel and Naomi swap one fruit chosen at random from their bags. (a) Derive an expression for the probability that Hazel will have I: + 1 kumquats today given that she had It kumquats yesterday. (b) Derive an expression for the probability that Hazel will have I: kumqu ats today given that she had It kumquats yesterday. (c) Derive an expression for the probability that Hazel will have R 1 kumquats today given that she had I: kumquats yesterday- (d) Give the transition matrix for the Markov process. (e) Is the Markov process irreducible? aperiodic? Prove your answers