Every day, Kymere takes the same street from his home to the university. There are multiple traffic lights with patterns along the way. If there is a green light while passing through an intersection, then 60% of the time the next light is also green and 25% of the time the next light is red. If the light is yellow, then there is a probability of 1 that the next light is red. If there is a red light, then 30% of the time the next light is green and 50% of the time the next light is red. (a) Does this situation represent a Markov Chain? Explain. (b) Set up the transition probability matrix and diagram. (c) The first light is green. Compute and interpret all probabilities after three more lights. (d) If Kymere has many street lights between home and the university, what proportion of these lights are green, yellow, and red? [No technology estimations permitted. Solve this problem with a system of equations showing every step and fraction answers only.]