5. (4 marks) On any given day, a system is in either State A or State B. If the system is in State A, the probability that it is in State B the following day is 0.2 (otherwise, it remains in State A). If the system is in State B, the probability that it is in State A the following day is 0.4 (otherwise, it remains in State B). a. (2 marks) If the system is in State A on Tuesday, what is the probability that it is also in State A on Wednesday and Thursday? b. (2 marks) Are the states on any two consecutive days independent? Explain. (8 marks) A real estate agent plans on showing 10 properties to her client: 5 condos, 3 townhouses, and 2 detached houses. She is deciding on the order in which to show the properties. a. (2 marks) From how many condo/townhouse/house orderings does the agent have to choose? (For this question, imagine that all the condos are identical, all the townhouses are identical, and all the houses are identical.) b. (3 marks) If the agent selects an ordering at random, what is the probability that she will show the 5 condos consecutively (one after the other)? c. (3 marks) The agent can show only 4 properties on a given day. If she chooses 4 of the properties at random to show on Saturday, what is the probabilility that exactly 2 are condos