3) 20 pts.] A spider hunting a fly moves between locations 1 and 2 according to a Markov Chain starting in location 1. The fly, unaware of the spider, starts in When Chain starting in locationLThead 0.7 0.3 0.3 0.7 with transition matrix location 2 and moves according to a Markov chain with transition matrix they meet in the same location, the spider catches the fly and the hunt ends. a) Show that the progress of the hunt, except for knowing the location where it ends, can be 0.4 0.6 0.6 0.4 described by a three-state Markov Chain where one absorbing state represents hunt ended and the other two states represent that the spider and fly are at different locations. (Define states, write the transition matrix and draw transition diagram for this chain.) b) Find the probability that after 3 moves (at time 3) the spider and fly are both at their initial locations. o) What is the average duration of the hunt